Handbook on the Physics and Chemistry of Rare Earths, Vol. 33

HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS VOLUME 33 HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS ...

Author: Editors: K. A. Gschneidner | Jr. | J.-C. G. Bunzli | and V. K.Pecharsky

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HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS VOLUME 33

HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS

Advisory Editorial Board G. ADACHI, Kobe, Japan W.J. EVANS, Irvine, USA S.M. KAUZLARICH, Davis, USA G.H. LANDER, Karlsruhe, Germany M.F. REID, Christchurch, New Zealand Editor Emeritus LeRoy EYRING, Tempe, USA

HANDBOOK ON THE PHYSICS AND CHEMISTRY OF

RARE EARTHS VOLUME 33

EDITORS

Karl A. GSCHNEIDNER, Jr. Ames Laboratory–US DOE, and Department of Materials Science and Engineering Iowa State University Ames, Iowa 50011-3020 USA

Jean-Claude G. BÜNZLI Swiss Federal Institute of Technology Institute of Molecular & Biological Chemistry BCH 1402 CH-1015 Lausanne Switzerland

Vitalij K. PECHARSKY Ames Laboratory–US DOE, and Department of Materials Science and Engineering Iowa State University Ames, Iowa 50011-3020 USA

2003

ELSEVIER AMSTERDAM, BOSTON, LONDON, NEW YORK, OXFORD, PARIS, SAN DIEGO, SAN FRANCISCO, SINGAPORE, SYDNEY, TOKYO

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Handbook on the Physics and Chemistry of Rare Earths Vol. 33 edited by K.A. Gschneidner, Jr., J.-C.G. Bünzli and V.K. Pecharsky © 2003 Elsevier Science B.V. All rights reserved

PREFACE Karl A. GSCHNEIDNER, Jr., Jean-Claude G. BÜNZLI, and Vitalij K. PECHARSKY

These elements perplex us in our rearches [sic], bafﬂe us in our speculations, and haunt us in our very dreams. They stretch like an unknown sea before us – mocking, mystifying, and murmuring strange revelations and possibilities. Sir William Crookes (February 16, 1887)

With this volume of the Handbook on the Physics and Chemistry of Rare Earth Profs. JeanClaude Bünzli, Swiss Federal Institute of Technology, Lausanne, and Vitalij K. Pecharsky, Iowa State University, Ames have joined Prof. Karl A. Gschneidner, Jr., one of the founding editors of this series, as editors. Readers of prior volumes of the Handbook will notice that the Preface format has changed with the inclusion of the title and author(s), plus an appropriate ﬁgure from each of the chapters, instead of just a brief summary of its contents. This volume of the Handbook illustrates the rich variety of topics covered by rare earth science. Three chapters are devoted to the description of solid state compounds: skutterudites (Chapter 211), rare earth-antimony systems (Chapter 212), and rare earth-manganese perovskites (Chapter 214). Two other reviews deal with solid state properties: one contribution includes information on existing thermodynamic data of lanthanide trihalides (Chapter 213) while the other one describes optical properties of rare earth compounds under pressure (Chapter 217). Finally, two chapters focus on solution chemistry. The state of the art in unraveling solution structure of lanthanide-containing coordination compounds by paramagnetic nuclear magnetic resonance is outlined in Chapter 215. The potential of time-resolved, laser-induced emission spectroscopy for the analysis of lanthanide and actinide solutions is presented and critically discussed in Chapter 216.

211 Filled Skutterudites by Brian C. Sales, Oak Ridge, National Laboratory, Tennessee, USA The lead chapter reviews the remarkable physical behaviors of a distinctive family of intermetallic compounds – the ﬁlled lanthanide skutterudites. These unique compounds, which have the RM4 X12 stoichiometry (where R = lanthanides, M = Fe, Ru, and Os, and X = P, As and Sb), are best known for their excellent high temperature (> 700 K) thermoelectric properties. But as Brian Sales points out, they also exhibit a rich variety of electronic and v

vi

PREFACE

magnetic ground states – heavy fermion mediated superconductivity, ferromagnetism, antiferromagnetism, hybridization gaps (Kondo insulator behavior), nonFermi-liquid behavior and quantum critical points, quadrupolar ordering, and ﬁeld-induced heavy fermion states. The Ce-based phases exhibit: heavy fermion behavior – CeFe4 Sb12 ; non-Fermi liquid behavior and possibly a quantum critical point – CeRu4 Sb12; and narrow (hybridized) gap semiconducting behavior – CeM4 P12 (M = Fe, Ru, Os). However, the most exotic lanthanide skutterudite is PrFe4 P12 because it has both quadrupole order and heavy fermion ground states, which are extremely close in energy. At low temperatures, < 6 K, a magnetic ﬁeld of 4 T can drive PrFe4 P12 between the two ground states leading to some unusual physical properties. Superconductivity is observed in most LaM4 X12 phases, as well as two of the Pr skutterudites, while those containing Nd, Eu, Gd and Tb exhibit magnetic ordering. Interestingly enough, EuFe4 P12 has the highest ferromagnetic ordering temperature, 100 K, of the RM 4 X12 compounds.

212 Rare Earth-Antimony Systems by Oksana Sologub, University of Wien, Austria, Petro Salamakha, Institute of Nuclear Technology, Sacavem, Portugal An extensive compilation of the structural and physical properties of rare earth-antimony and of some rare earth-uranium-antimony systems is presented. The ﬁrst part of the review collects the phase diagrams of binary R–M and ternary R–M–Sb, R–R –Sb or R–U–Sb metal antimonides, along with their crystallographic data and the experimental synthetic methods used to isolate the compounds. A few quaternary systems are also presented. The chapter then focuses on the properties of ternary systems. Atomic coordinates are given for more than forty types of crystal structures, and magnetic susceptibility and resistivity data are tabulated. The chapter ends with a general discussion on the peculiarities of the rare earthantimony interaction. The binary systems have been systematically studied and usually yield stoichiometric compounds, R5 Sb3 , R4 Sb3 , RSb, and RSb2 . Ternary systems are less well known, so that general trends are more difﬁcult to determine, but several families of ternary antimonides crystallize with structures derived from those of binary types.

PREFACE

vii

213 Thermodynamic Properties of the Lanthanide (III) Halides by Rudy I. M. Konings and A. Kovács, Institute of Transuranium Elements, Karlsruhe, Germany The trivalent lanthanide halides have had and still have an important technological relevance. In the 1950s and 1960s, ﬂuorides were studied within the frame of the molten salt nuclear reactor project and a pyrochemical process was developed for the reprocessing of metal fuel. Nowadays, these technologies ﬁnd a renewed interest within the frame of actinide-lanthanide separation for nuclear waste management. Moreover, chlorides, bromides and iodides are ﬁnding application in lighting industry to improve the performances of highpressure discharge lamps. The authors describe the thermodynamic properties of lanthanide halides in a thorough review, which emphasizes the major trends in the data. Polymorphism, low- and high-temperature heat capacity and the enthalpy of formation of the solid state trihalides are presented ﬁrst while the last sections of the review deal with heat capacity of the liquids and the heat capacity and enthalpy of formation of the gaseous trihalides.

214 Rare Earth-Manganese Perovskites by John B. Goodenough, University of Texas at Austin, USA Rare earth ions inﬂuence the physical properties of rare earth-manganese perovskites R1−x Ax MnO3 (where A is an alkaline earth cation) through a geometric factor, which determines the bending of the Mn–O–Mn angle in order to achieve a match between the Mn–O and A–O equilibrium bond lengths. The author describes how this inﬂuence, along with other subtle electronic effects due to the Jahn-Teller distortion and to interactions with σ -bonding electrons, may be used to design materials with unusual physical properties (e.g., magnetization, resistivity, thermal conductivity) that may prove technologically useful. The chapter starts with essential concepts related to structural aspects (the so-called tolerance factor) and electronic considerations, such as ligand-ﬁeld effects, interatomic interactions and localized-itinerant electronic transitions. For instance, constraining the itinerant electrons to two-dimensional planes or one-dimensional chains, restricts ferromagnetic double-exchange coupling to the metallic planes or chains. Following this introductory part, both single- and double-valent perovskites are comprehensively reviewed taking these concepts into consideration.

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215 Paramagnetic NMR Lanthanide Induced Shift for Extracting Solution Structure by Claude Piguet, University of Geneva, Switzerland, Carlos F.G.C. Geraldes, University of Coimbra, Portugal

n

n 2m m Fim Sz j + B0 Gi Cj

The authors summarize the latest advances in one fascinating technique enabling chemists to unm=l m=l ravel the solution structures of coordination and supramolecular compounds, nuclear magnetic resonance of paramagnetic species. While paramagnetism is often considered as being a handicap to interpret NMR spectra, detailed structural and electronic information can be extracted from the separation of the contact and pseudo-contact contributions to the paramagnetic NMR shifts induced by the presence of a lanthanide ion. In a precedent chapter of the Handbook (ch. 153, vol. 23), John Forsberg has reported on the use of a one-nucleus method for determining the structure of axial compounds. Here, the authors outline the general theory and then focus on the limitations of Bleaney’s approach for modeling paramagnetic anisotropies and on the description of the new two- and three-nuclei methods, which are independent of changes in crystal ﬁeld parameters and hyperﬁne coupling constants. A comprehensive survey of the application of these methods to coordination and supramolecular compounds with three- and fourfold symmetry is presented. para

δij

216 Lanthanide and Actinide Solution Chemistry Studied by Time-Resolved Emission Spectroscopy by Isabelle Billard, Institut de Recherches Subatomiques, Strasbourg, France Time-resolved emission spectroscopy is gaining importance in the study of various chemical aspects of luminescent lanthanide and actinide ions in solution. Here, the author describes the theoretical background of this analytical technique and discusses potential applications. Changes in the solution composition and/or in the metal-ion inner coordination sphere induce modiﬁcations of the spectroscopic properties of the luminescent species. Both time-resolved spectra and luminescence decays convey useful information. Several models, which are commonly used to extract physico-chemical information from the spectroscopic data, are presented and critically compared. Applications of time-resolved emission spectroscopy are numerous and range from the characterization of the

PREFACE

ix

metal ion solvation sphere, to the evaluation of reaction rate constants and equilibrium constants, and to the quantitative determination of ultra trace amounts of lanthanide and actinide ions in solution, an aspect of importance in environmental chemistry. Potential uses of the technique to study micellar systems and ionic liquids are outlined.

217 Optical Studies on Non-Metallic Rare Earth Compounds under Pressure by Thomas Tröster, University of Paderborn, Germany In a captivating review, the author surveys the optical properties of non-metallic compounds under pressure. The relationship between the optical properties of compounds and their microscopic structure has always triggered a lot of interest and has been regarded as a fundamental problem. Rare earth ions with partially ﬁlled 4f shells provide a detailed ﬁngerprint of the surrounding arrangement of atoms and their interaction with f-electrons. Minute effects can be evidenced by measuring the spectra in various hosts lattices. However, the presence of impurities somewhat limits the usefulness of the empirical data. In contrast, applying high-pressure to a system usually induces continuous variations in parameters, such as interatomic distances, inﬂuencing the optical properties. That is, the experimentalists can alter the energy difference between two states, almost at will, henceforth gathering information on their mutual inﬂuence. High pressure techniques are described and experimental data on energy levels, crystal ﬁeld splittings, intensities and lifetimes of f-f transitions, as well as on electron–phonon interactions, are surveyed.

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CONTENTS Preface v Contents xi Contents of Volumes 1–32 xiii 211. Brian C. Sales Filled skutterudites 1 212. Oksana L. Sologub and Petro S. Salamakha Rare earth –antimony systems 35 213. R.J.M. Konings and A. Kovács Thermodynamic properties of the lanthanide(III) halides 147 214. John B. Goodenough Rare earth –manganese perovskites

249

215. Claude Piguet and Carlos F.G.C. Geraldes Paramagnetic NMR lanthanide induced shifts for extracting solution structures

353

216. Isabelle Billard Lanthanide and actinide solution chemistry as studied by time-resolved emission spectroscopy 465 217. Thomas Tröster Optical studies of non-metallic compounds under pressure 515 Author index

591

Subject index 637

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CONTENTS OF VOLUMES 1–32 VOLUME 1: Metals 1978, 1st repr. 1982, 2nd repr. 1991; ISBN 0-444-85020-1 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

Z.B. Goldschmidt, Atomic properties (free atom) 1 B.J. Beaudry and K.A. Gschneidner Jr, Preparation and basic properties of the rare earth metals 173 S.H. Liu, Electronic structure of rare earth metals 233 D.C. Koskenmaki and K.A. Gschneidner Jr, Cerium 337 L.J. Sundström, Low temperature heat capacity of the rare earth metals 379 K.A. McEwen, Magnetic and transport properties of the rare earths 411 S.K. Sinha, Magnetic structures and inelastic neutron scattering: metals, alloys and compounds 489 T.E. Scott, Elastic and mechanical properties 591 A. Jayaraman, High pressure studies: metals, alloys and compounds 707 C. Probst and J. Wittig, Superconductivity: metals, alloys and compounds 749 M.B. Maple, L.E. DeLong and B.C. Sales, Kondo effect: alloys and compounds 797 M.P. Dariel, Diffusion in rare earth metals 847 Subject index 877

VOLUME 2: Alloys and intermetallics 1979, 1st repr. 1982, 2nd repr. 1991; ISBN 0-444-85021-X 13. 14. 15. 16. 17. 18. 19. 20.

A. Iandelli and A. Palenzona, Crystal chemistry of intermetallic compounds 1 H.R. Kirchmayr and C.A. Poldy, Magnetic properties of intermetallic compounds of rare earth metals A.E. Clark, Magnetostrictive RFe2 intermetallic compounds 231 J.J. Rhyne, Amorphous magnetic rare earth alloys 259 P. Fulde, Crystal ﬁelds 295 R.G. Barnes, NMR, EPR and Mössbauer effect: metals, alloys and compounds 387 P. Wachter, Europium chalcogenides: EuO, EuS, EuSe and EuTe 507 A. Jayaraman, Valence changes in compounds 575 Subject index 613

VOLUME 3: Non-metallic compounds –I 1979, 1st repr. 1984; ISBN 0-444-85215-8 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.

L.A. Haskin and T.P. Paster, Geochemistry and mineralogy of the rare earths 1 J.E. Powell, Separation chemistry 81 C.K. Jørgensen, Theoretical chemistry of rare earths 111 W.T. Carnall, The absorption and ﬂuorescence spectra of rare earth ions in solution L.C. Thompson, Complexes 209 G.G. Libowitz and A.J. Maeland, Hydrides 299 L. Eyring, The binary rare earth oxides 337 D.J.M. Sevan and E. Summerville, Mixed rare earth oxides 401 C.P. Khattak and F.F.Y. Wang, Perovskites and garnets 525 L.H. Brixner, J.R. Barkley and W. Jeitschko, Rare earth molybdates (VI) 609 Subject index 655 xiii

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VOLUME 4: Non-metallic compounds –II 1979, 1st repr. 1984; ISBN 0-444-85216-6 31. 32. 33. 34. 35. 36. 37A. 37B. 37C. 37D. 37E. 37F. 37G.

J. Flahaut, Sulﬁdes, selenides and tellurides 1 J.M. Haschke, Halides 89 F. Hulliger, Rare earth pnictides 153 G. Blasse, Chemistry and physics of R-activated phosphors 237 M.J. Weber, Rare earth lasers 275 F.K. Fong, Nonradiative processes of rare-earth ions in crystals 317 J.W. O’Laughlin, Chemical spectrophotometric and polarographic methods 341 S.R. Taylor, Trace element analysis of rare earth elements by spark source mass spectroscopy 359 R.J. Conzemius, Analysis of rare earth matrices by spark source mass spectrometry 377 E.L. DeKalb and V.A. Fassel, Optical atomic emission and absorption methods 405 A.P. D’Silva and V.A. Fassel, X-ray excited optical luminescence of the rare earths 441 F.W.V. Boynton, Neutron activation analysis 457 S. Schuhmann and J.A. Philpotts, Mass-spectrometric stable-isotope dilution analysis for lanthanides in geochemical materials 471 38. J. Reuben and G.A. Elgavish, Shift reagents and NMR of paramagnetic lanthanide complexes 483 39. J. Reuben, Bioinorganic chemistry: lanthanides as probes in systems of biological interest 515 40. T.J. Haley, Toxicity 553 Subject index 587

VOLUME 5 1982, 1st repr. 1984; ISBN 0-444-86375-3 41. M. Gasgnier, Rare earth alloys and compounds as thin ﬁlms 1 42. E. Gratz and M.J. Zuckermann, Transport properties (electrical resitivity, thermoelectric power thermal conductivity) of rare earth intermetallic compounds 117 43. F.P. Netzer and E. Bertel, Adsorption and catalysis on rare earth surfaces 217 44. C. Boulesteix, Defects and phase transformation near room temperature in rare earth sesquioxides 321 45. O. Greis and J.M. Haschke, Rare earth ﬂuorides 387 46. C.A. Morrison and R.P. Leavitt, Spectroscopic properties of triply ionized lanthanides in transparent host crystals 461 Subject index 693 VOLUME 6 1984; ISBN 0-444-86592-6 47. K.H.J. Buschow, Hydrogen absorption in intermetallic compounds 1 48. E. Parthé and B. Chabot, Crystal structures and crystal chemistry of ternary rare earth–transition metal borides, silicides and homologues 113 49. P. Rogl, Phase equilibria in ternary and higher order systems with rare earth elements and boron 335 50. H.B. Kagan and J.L. Namy, Preparation of divalent ytterbium and samarium derivatives and their use in organic chemistry 525 Subject index 567 VOLUME 7 1984; ISBN 0-444-86851-8 51. P. Rogl, Phase equilibria in ternary and higher order systems with rare earth elements and silicon 52. K.H.J. Buschow, Amorphous alloys 265 53. H. Schumann and W. Genthe, Organometallic compounds of the rare earths 446 Subject index 573

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VOLUME 8 1986; ISBN 0-444-86971-9 54. K.A. Gschneidner Jr and F.W. Calderwood, Intra rare earth binary alloys: phase relationships, lattice parameters and systematics 1 55. X. Gao, Polarographic analysis of the rare earths 163 56. M. Leskelä and L. Niinistö, Inorganic complex compounds I 203 57. J.R. Long, Implications in organic synthesis 335 Errata 375 Subject index 379 VOLUME 9 1987; ISBN 0-444-87045-8 58. 59. 60. 61.

R. Reisfeld and C.K. Jørgensen, Excited state phenomena in vitreous materials 1 L. Niinistö and M. Leskelä, Inorganic complex compounds II 91 J.-C.G. Bünzli, Complexes with synthetic ionophores 321 Zhiquan Shen and Jun Ouyang, Rare earth coordination catalysis in stereospeciﬁc polymerization Errata 429 Subject index 431

395

VOLUME 10: High energy spectroscopy 1988; ISBN 0-444-87063-6 62. Y. Baer and W.-D. Schneider, High-energy spectroscopy of lanthanide materials – An overview 1 63. M. Campagna and F.U. Hillebrecht, f-electron hybridization and dynamical screening of core holes in intermetallic compounds 75 64. O. Gunnarsson and K. Schönhammer, Many-body formulation of spectra of mixed valence systems 103 65. A.J. Freeman, B.I. Min and M.R. Norman, Local density supercell theory of photoemission and inverse photoemission spectra 165 66. D.W. Lynch and J.H. Weaver, Photoemission of Ce and its compounds 231 67. S. Hüfner, Photoemission in chalcogenides 301 68. J.F. Herbst and J.W. Wilkins, Calculation of 4f excitation energies in the metals and relevance to mixed valence systems 321 69. B. Johansson and N. Mårtensson, Thermodynamic aspects of 4f levels in metals and compounds 361 70. F.U. Hillebrecht and M. Campagna, Bremsstrahlung isochromat spectroscopy of alloys and mixed valent compounds 425 71. J. Röhler, X-ray absorption and emission spectra 453 72. F.P. Netzer and J.A.D. Matthew, Inelastic electron scattering measurements 547 Subject index 601 VOLUME 11: Two-hundred-year impact of rare earths on science 1988; ISBN 0-444-87080-6 73. 74. 75. 76. 77. 78. 79.

H.J. Svec, Prologue 1 F. Szabadváry, The history of the discovery and separation of the rare earths 33 B.R. Judd, Atomic theory and optical spectroscopy 81 C.K. Jørgensen, Inﬂuence of rare earths on chemical understanding and classiﬁcation 197 J.J. Rhyne, Highlights from the exotic phenomena of lanthanide magnetism 293 B. Bleaney, Magnetic resonance spectroscopy and hyperﬁne interactions 323 K.A. Gschneidner Jr and A.H. Daane, Physical metallurgy 409 S.R. Taylor and S.M. McLennan, The signiﬁcance of the rare earths in geochemistry and cosmochemistry Errata 579 Subject index 581

485

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VOLUME 12 1989; ISBN 0-444-87105-5 80. 81. 82. 83. 84. 85. 86. 87.

J.S. Abell, Preparation and crystal growth of rare earth elements and intermetallic compounds 1 Z. Fisk and J.P. Remeika, Growth of single crystals from molten metal ﬂuxes 53 E. Burzo and H.R. Kirchmayr, Physical properties of R2 Fe14 B-based alloys 71 A. Szytuła and J. Leciejewicz, Magnetic properties of ternary intermetallic compounds of the RT2 X2 type H. Maletta and W. Zinn, Spin glasses 213 J. van Zytveld, Liquid metals and alloys 357 M.S. Chandrasekharaiah and K.A. Gingerich, Thermodynamic properties of gaseous species 409 W.M. Yen, Laser spectroscopy 433 Subject index 479

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VOLUME 13 1990; ISBN 0-444-88547-1 88. E.I. Gladyshevsky, O.I. Bodak and V.K. Pecharsky, Phase equilibria and crystal chemistry in ternary rare earth systems with metallic elements 1 89. A.A. Eliseev and G.M. Kuzmichyeva, Phase equilibrium and crystal chemistry in ternary rare earth systems with chalcogenide elements 191 90. N. Kimizuka, E. Takayama-Muromachi and K. Siratori, The systems R2 O3 –M2 O3 –M O 283 91. R.S. Houk, Elemental analysis by atomic emission and mass spectrometry with inductively coupled plasmas 385 92. P.H. Brown, A.H. Rathjen, R.D. Graham and D.E. Tribe, Rare earth elements in biological systems 423 Errata 453 Subject index 455 VOLUME 14 1991; ISBN 0-444-88743-1 93. 94. 95. 96. 97.

R. Osborn, S.W. Lovesey, A.D. Taylor and E. Balcar, Intermultiplet transitions using neutron spectroscopy E. Dormann, NMR in intermetallic compounds 63 E. Zirngiebl and G. Güntherodt, Light scattering in intermetallic compounds 163 P. Thalmeier and B. Lüthi, The electron–phonon interaction in intermetallic compounds 225 N. Grewe and F. Steglich, Heavy fermions 343 Subject index 475

1

VOLUME 15 1991; ISBN 0-444-88966-3 98. 99. 100. 101. 102.

J.G. Sereni, Low-temperature behaviour of cerium compounds 1 G.-y. Adachi, N. Imanaka and Zhang Fuzhong, Rare earth carbides 61 A. Simon, Hj. Mattausch, G.J. Miller, W. Bauhofer and R.K. Kremer, Metal-rich halides 191 R.M. Almeida, Fluoride glasses 287 K.L. Nash and J.C. Sullivan, Kinetics of complexation and redox reactions of the lanthanides in aqueous solutions 347 103. E.N. Rizkalla and G.R. Choppin, Hydration and hydrolysis of lanthanides 393 104. L.M. Vallarino, Macrocycle complexes of the lanthanide(III) yttrium(III) and dioxouranium(VI) ions from metal-templated syntheses 443 Errata 513 Subject index 515

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MASTER INDEX, Vols. 1–15 1993; ISBN 0-444-89965-0 VOLUME 16 1993; ISBN 0-444-89782-8 105. 106. 107. 108. 109.

M. Loewenhaupt and K.H. Fischer, Valence-ﬂuctuation and heavy-fermion 4f systems 1 I.A. Smirnov and V.S. Oskotski, Thermal conductivity of rare earth compounds 107 M.A. Subramanian and A.W. Sleight, Rare earths pyrochlores 225 R. Miyawaki and I. Nakai, Crystal structures of rare earth minerals 249 D.R. Chopra, Appearance potential spectroscopy of lanthanides and their intermetallics 519 Author index 547 Subject index 579

VOLUME 17: Lanthanides/Actinides: Physics –I 1993; ISBN 0-444-81502-3 110. M.R. Norman and D.D. Koelling, Electronic structure, Fermi surfaces, and superconductivity in f electron metals 1 111. S.H. Liu, Phenomenological approach to heavy-fermion systems 87 112. B. Johansson and M.S.S. Brooks, Theory of cohesion in rare earths and actinides 149 113. U. Benedict and W.B. Holzapfel, High-pressure studies – Structural aspects 245 114. O. Vogt and K. Mattenberger, Magnetic measurements on rare earth and actinide monopnictides and monochalcogenides 301 115. J.M. Fournier and E. Gratz, Transport properties of rare earth and actinide intermetallics 409 116. W. Potzel, G.M. Kalvius and J. Gal, Mössbauer studies on electronic structure of intermetallic compounds 539 117. G.H. Lander, Neutron elastic scattering from actinides and anomalous lanthanides 635 Author index 711 Subject index 753 VOLUME 18: Lanthanides/Actinides: Chemistry 1994; ISBN 0-444-81724-7 118. G.T. Seaborg, Origin of the actinide concept 1 119. K. Balasubramanian, Relativistic effects and electronic structure of lanthanide and actinide molecules 29 120. J.V. Beitz, Similarities and differences in trivalent lanthanide- and actinide-ion solution absorption spectra and luminescence studies 159 121. K.L. Nash, Separation chemistry for lanthanides and trivalent actinides 197 122. L.R. Morss, Comparative thermochemical and oxidation – reduction properties of lanthanides and actinides 239 123. J.W. Ward and J.M. Haschke, Comparison of 4f and 5f element hydride properties 293 124. H.A. Eick, Lanthanide and actinide halides 365 125. R.G. Haire and L. Eyring, Comparisons of the binary oxides 413 126. S.A. Kinkead, K.D. Abney and T.A. O’Donnell, f-element speciation in strongly acidic media: lanthanide and mid-actinide metals, oxides, ﬂuorides and oxide ﬂuorides in superacids 507 127. E.N. Rizkalla and G.R. Choppin, Lanthanides and actinides hydration and hydrolysis 529 128. G.R. Choppin and E.N. Rizkalla, Solution chemistry of actinides and lanthanides 559 129. J.R. Dufﬁeld, D.M. Taylor and D.R. Williams, The biochemistry of the f-elements 591 Author index 623 Subject index 659

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VOLUME 19: Lanthanides/Actinides: Physics –II 1994; ISBN 0-444-82015-9 130. E. Holland-Moritz and G.H. Lander, Neutron inelastic scattering from actinides and anomalous lanthanides 1 131. G. Aeppli and C. Broholm, Magnetic correlations in heavy-fermion systems: neutron scattering from single crystals 123 132. P. Wachter, Intermediate valence and heavy fermions 177 133. J.D. Thompson and J.M. Lawrence, High pressure studies – Physical properties of anomalous Ce, Yb and U compounds 383 134. C. Colinet and A. Pasturel, Thermodynamic properties of metallic systems 479 Author index 649 Subject index 693 VOLUME 20 1995; ISBN 0-444-82014-0 ¯ 135. Y. Onuki and A. Hasegawa, Fermi surfaces of intermetallic compounds 1 136. M. Gasgnier, The intricate world of rare earth thin ﬁlms: metals, alloys, intermetallics, chemical compounds, . . . 105 137. P. Vajda, Hydrogen in rare-earth metals, including RH2+x phases 207 138. D. Gignoux and D. Schmitt, Magnetic properties of intermetallic compounds 293 Author index 425 Subject index 457 VOLUME 21 1995; ISBN 0-444-82178-3 139. 140. 141. 142. 143. 144. 145. 146.

R.G. Bautista, Separation chemistry 1 B.W. Hinton, Corrosion prevention and control 29 N.E. Ryan, High-temperature corrosion protection 93 T. Sakai, M. Matsuoka and C. Iwakura, Rare earth intermetallics for metal–hydrogen batteries 133 G.-y. Adachi and N. Imanaka, Chemical sensors 179 D. Garcia and M. Faucher, Crystal ﬁeld in non-metallic (rare earth) compounds 263 J.-C.G. Bünzli and A. Milicic-Tang, Solvation and anion interaction in organic solvents 305 V. Bhagavathy, T. Prasada Rao and A.D. Damodaran, Trace determination of lanthanides in high-purity rareearth oxides 367 Author index 385 Subject index 411

VOLUME 22 1996; ISBN 0-444-82288-7 147. C.P. Flynn and M.B. Salamon, Synthesis and properties of single-crystal nanostructures 1 148. Z.S. Shan and D.J. Sellmyer, Nanoscale rare earth–transition metal multilayers: magnetic structure and properties 81 149. W. Suski, The ThMn12 -type compounds of rare earths and actinides: structure, magnetic and related properties 143 150. L.K. Aminov, B.Z. Malkin and M.A. Teplov, Magnetic properties of nonmetallic lanthanide compounds 295 151. F. Auzel, Coherent emission in rare-earth materials 507 152. M. Dolg and H. Stoll, Electronic structure calculations for molecules containing lanthanide atoms 607 Author index 731 Subject index 777

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VOLUME 23 1996; ISBN 0-444-82507-X 153. 154. 155. 156. 157. 158.

J.H. Forsberg, NMR studies of paramagnetic lanthanide complexes and shift reagents 1 N. Sabbatini, M. Guardigli and I. Manet, Antenna effect in encapsulation complexes of lanthanide ions C. Görller-Walrand and K. Binnemans, Rationalization of crystal-ﬁeld parametrization 121 Yu. Kuz’ma and S. Chykhrij, Phosphides 285 S. Boghosian and G.N. Papatheodorou, Halide vapors and vapor complexes 435 R.H. Byrne and E.R. Sholkovitz, Marine chemistry and geochemistry of the lanthanides 497 Author index 595 Subject index 631

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VOLUME 24 1997; ISBN 0-444-82607-6 159. 160. 161. 162. 163. 164.

P.A. Dowben, D.N. McIlroy and Dongqi Li, Surface magnetism of the lanthanides 1 P.G. McCormick, Mechanical alloying and mechanically induced chemical reactions 47 A. Inoue, Amorphous, quasicrystalline and nanocrystalline alloys in Al- and Mg-based systems 83 B. Elschner and A. Loidl, Electron-spin resonance on localized magnetic moments in metals 221 N.H. Duc, Intersublattice exchange coupling in the lanthanide–transition metal intermetallics 339 R.V. Skolozdra, Stannides of rare-earth and transition metals 399 Author index 519 Subject index 559

VOLUME 25 1998; ISBN 0-444-82871-0 165. 166. 167. 168.

H. Nagai, Rare earths in steels 1 R. Marchand, Ternary and higher order nitride materials 51 C. Görller-Walrand and K. Binnemans, Spectral intensities of f–f transitions 101 G. Bombieri and G. Paolucci, Organometallic π complexes of the f-elements 265 Author index 415 Subject index 459

VOLUME 26 1999; ISBN 0-444 50815-1 169. D.F. McMorrow, D. Gibbs and J. Bohr, X-ray scattering studies of lanthanide magnetism 1 170. A.M. Tishin, Yu.I. Spichkin and J. Bohr, Static and dynamic stresses 87 171. N.H. Duc and T. Goto, Itinerant electron metamagnetism of Co sublattice in the lanthanide–cobalt intermetallics 177 172. A.J. Arko, P.S. Riseborough, A.B. Andrews, J.J. Joyce, A.N. Tahvildar-Zadeh and M. Jarrell, Photoelectron spectroscopy in heavy fermion systems: Emphasis on single crystals 265 Author index 383 Subject index 405 VOLUME 27 1999; ISBN 0-444-50342-0 173. P.S. Salamakha, O.L. Sologub and O.I. Bodak, Ternary rare-earth–germanium systems 1 174. P.S. Salamakha, Crystal structures and crystal chemistry of ternary rare-earth germanides 225 175. B. Ya. Kotur and E. Gratz, Scandium alloy systems and intermetallics 339 Author index 535 Subject index 553

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VOLUME 28 2000; ISBN 0-444-50346-3 176. 177. 178. 179. 180.

J.-P. Connerade and R.C. Karnatak, Electronic excitation in atomic species 1 G. Meyer and M.S. Wickleder, Simple and complex halides 53 R.V. Kumar and H. Iwahara, Solid electrolytes 131 A. Halperin, Activated thermoluminescence (TL) dosimeters and related radiation detectors 187 K.L. Nash and M.P. Jensen, Analytical separations of the lanthanides: basic chemistry and methods Author index 373 Subject index 401

311

VOLUME 29: The role of rare earths in catalysis 2000; ISBN 0-444-50472-9 181. 182. 183. 184. 185. 186.

P. Maestro, Foreword 1 V. Paul-Boncour, L. Hilaire and A. Percheron-Guégan, The metals and alloys in catalysis 5 H. Imamura, The metals and alloys (prepared utilizing liquid ammonia solutions) in catalysis II M.A. Ulla and E.A. Lombardo, The mixed oxides 75 J. Kašpar, M. Graziani and P. Fornasiero, Ceria-containing three-way catalysts 159 A. Corma and J.M. López Nieto, The use of rare-earth-containing zeolite catalysts 269 S. Kobayashi, Triﬂates 315 Author index 377 Subject index 409

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VOLUME 30: High-Temperature Superconductors –I 2000; ISBN 0-444-50528-8 187. 188. 189. 190. 191.

M.B. Maple, High-temperature superconductivity in layered cuprates: overview 1 B. Raveau, C. Michel and M. Hervieu, Crystal chemistry of superconducting rare-earth cuprates 31 Y. Shiohara and E.A. Goodilin, Single-crystal growth for science and technology 67 P. Karen and A. Kjekshus, Phase diagrams and thermodynamic properties 229 B. Elschner and A. Loidl, Electron paramagnetic resonance in cuprate superconductors and in parent compounds 375 192. A.A. Manuel, Positron annihilation in high-temperature superconductors 417 193. W.E. Pickett and I.I. Mazin, RBa2 Cu3 O7 compounds: electronic theory and physical properties 453 194. U. Staub and L. Soderholm, Electronic 4f state splittings in cuprates 491 Author index 547 Subject index 621 VOLUME 31: High-Temperature Superconductors –II 2001; ISBN 0-444-50719-1 195. E. Kaldis, Oxygen nonstoichiometry and lattice effects in YBa2 Cu3 Ox . Phase transitions, structural distortions and phase separation 1 196. H.W. Weber, Flux pinning 187 197. C.C. Almasan and M.B. Maple, Magnetoresistance and Hall effect 251 198. T.E. Mason, Neutron scattering studies of spin ﬂuctuations in high-temperature superconductors 281 199. J.W. Lynn and S. Skanthakumar, Neutron scattering studies of lanthanide magnetic ordering 315 200. P.M. Allenspach and M.B. Maple, Heat capacity 351 201. M. Schabel and Z.-X. Shen, Angle-resolved photoemission studies of untwinned yttrium barium copper oxide 391 202. D.N. Basov and T. Timusk, Infrared properties of high-Tc superconductors: an experimental overview 437 203. S.L. Cooper, Electronic and magnetic Raman scattering studies of the high-Tc cuprates 509

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204. H. Sugawara, T. Hasegawa and K. Kitazawa, Characterization of cuprate superconductors using tunneling spectra and scanning tunneling microscopy 563 Author index 609 Subject index 677 VOLUME 32 2001; ISBN 0-444-50762-0 205. N.H. Duc, Giant magnetostriction in lanthanide–transition metal thin ﬁlms 1 206. G.M. Kalvius, D.R. Noakes and O. Hartmann, μSR studies of rare-earth and actinide magnetic materials 55 207. Rainer Pöttgen, Dirk Johrendt and Dirk Kußmann, Structure–property relations of ternary equiatomic YbTX intermetallics 453 208. Kurima Kobayashi and Satoshi Hirosawa, Permanent magnets 515 209. I.G. Vasilyeva, Polysulﬁdes 567 210. Dennis K.P. Ng, Jianzhuang Jiang, Kuninobu Kasuga and Kenichi Machida, Half-sandwich tetrapyrrole complexes of rare earths and actinides 611 Author index 655 Subject index 733

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Handbook on the Physics and Chemistry of Rare Earths Vol. 33 edited by K.A. Gschneidner, Jr., J.-C.G. Bünzli and V.K. Pecharsky © 2003 Elsevier Science B.V. All rights reserved

Chapter 211 FILLED SKUTTERUDITES Brian C. SALES Solid State Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6056, USA

Contents

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

List of symbols List of acronyms Introduction Structure Lanthanide skutterudites as Zintl compounds Synthesis and crystal growth La ﬁlled skutterudites Ce ﬁlled skutterudites Pr ﬁlled skutterudites Nd ﬁlled skutterudites Sm ﬁlled skutterudites Eu ﬁlled skutterudites

1 2 2 3 5 6 8 12 17 22 23 23

11. 12. 13. 14.

Gd ﬁlled skutterudites Tb ﬁlled skutterudites Yb ﬁlled skutterudites Filled skutterudite thermoelectrics 14.1. Introduction to thermoelectric materials and devices 14.2. Electron crystals and phonon glasses 14.3. Future of ﬁlled skutterudites as thermoelectrics 15. Concluding remarks Acknowledgements References

List of symbols Beq

isotropic ADP

T

temperature

C CRLM

heat capacity heat capacity from resonant level model

T TAF

magnetic ﬁeld in Tesla antiferromagnetic ordering temperature

Cph

heat capacity from phonons

Tc

superconducting transition temperature

eg H

doubly degenerate 3d orbitals magnetic ﬁeld

Tco Td

cold temperature of thermoelectric device displacive ordering transition

kB

Boltzmann constant

TFM

ferromagnetic ordering temperature

k me

wavevector free electron mass

triply degenerate 3d orbitals hot temperature of thermoelectric device

m∗ n-type

t2g Th

effective electron mass electron doped semiconductor

TK T∗

Kondo temperature characteristic temperature

P

pressure

T0

characteristic temperature

p-type RW

hole doped semiconductor Wilson–Sommerfeld ratio

μB μeff

Bohr magneton effective magnetic moment

S

Seebeck coefﬁcient

Z

thermoelectric ﬁgure of merit

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ZT

dimensionless thermoelectric ﬁgure of merit

κ

total thermal conductivity of solid

γ Γ

electronic coefﬁcient of heat capacity (1 + ZT)1/2

κe κL

thermal conductivity of electrons or holes thermal conductivity of lattice

Γ1 Γ3

crystal ﬁeld singlet non-Kramers doublet (crystal ﬁeld state)

κmin ρ

minimum lattice thermal conductivity electrical resistivity

Γ4

crystal ﬁeld triplet

ΘD

Debye temperature

Γ5 Δ

crystal ﬁeld triplet hybridization gap

χ χ0

magnetic susceptibility magnetic susceptibility at T = 0

ΔC

jump in heat capacity at Tc

List of acronyms ADP AFM

atomic displacement parameters antiferromagnetic metal

HFSC LDA

heavy-fermion superconductor local density approximation

BCS CEF

theory of superconductivity crystalline electric ﬁeld

M M-I

metal metal to insulator transition

dHvA

de Hass–van Alphen

NFL

non-Fermi liquid

DOS density of states FIHFM ﬁeld-induced heavy-fermion metal

ODS QCP

ordered state quantum critical point

FMM

ferromagnetic metal

QO

quadrupolar order

HFS HFM

heavy-fermion state heavy-fermion metal

RRR SC

residual resistance ratio superconductor

HGS

hybridization gap semiconductor

XANES X-ray absorption near edge spectroscopy

1. Introduction Skutterudite is the name of a CoAs3 -based mineral that was ﬁrst extensively mined as a source of cobalt and nickel in the region of Skutterud Norway. Compounds with the same cubic crystal structure have since been known as “skutterudites”. Oftedal ﬁrst extensively studied the skutterudite crystal structure in 1928 (Oftedal, 1928). An example of a well-formed natural skutterudite mineral is shown in ﬁg. 1. The skutterudite structure has two voids in each unit cell that are large enough to accommodate a variety of atoms including most of the light lanthanides (La, Ce, Pr, Nd, Sm, Eu, Gd, Tb) and Yb. The ﬁrst “ﬁlled skutterudites” were synthesized by Prof. Jeitschko and collaborators in the late 1970s (Jeitschko and Braun, 1977; Braun and Jeitschko, 1980a, 1980b, 1980c). The chemical composition of the lanthanide ﬁlled skutterudites is given by RM4 X12 , where R are the lanthanides noted above, M = Fe, Ru, Os and X = P, As, Sb. For each lanthanide element there is a maximum of nine distinct compounds with the skutterudite structure. In 1996 it was found that some of the lanthanide skutterudites had excellent thermoelectric properties above room temperature (Sales et al., 1996;

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Fig. 1. Photograph of a natural skutterudite mineral. This extremely well crystallized specimen is from the Sandroste Mine near Bou Azzer, Morocco. (Image downloaded from Carnegie–Mellon Mineral Collection Images, Alan Guisewite’s collection.)

Fleurial et al., 1996) and this greatly increased the interest in these materials for thermoelectric applications. In addition to the stoichiometric ﬁlled skutterudite compounds of the form RM4 X12 , a large number of related alloys were also investigated as possible thermoelectric materials. Most of the research on lanthanide skutterudites in the context of thermoelectric applications has been reviewed recently by Uher (2001), Nolas et al. (1999), and Sales (1998) and hence only a brief summary of the thermoelectric research will be presented at the end of this article. This chapter will focus on what is known about the structural, electronic and magnetic properties of the stoichiometric lanthanide skutterudite compounds of the form RM4 X12 . The low temperature properties will be of particular interest since these compounds exhibit a rich variety of electronic and magnetic ground states that include heavy-fermion-mediated superconductivity, ferromagnetism, antiferromagnetism, hybridization gaps (Kondo insulator behavior), non-Fermi-liquid behavior and quantum critical points, quadrupolar ordering, and ﬁeld-induced heavy-fermion states.

2. Structure The ﬁlled skutterudites crystallize in the cubic space group Im3 with two formula units (RM4 X12 ) per unit cell. There are three unique atomic positions in the normalized unit cell. The rare earth position is (0, 0, 0), the transition metal position is (0.25, 0.25, 0.25), and the pnicogen (P, As, Sb) position (0, y, z) is variable with y ≈ 0.35, z ≈ 0.16 (ﬁg. 2). The positions of the remaining 31 atoms in the unit cell are determined by the symmetry operations associated with the Im3 space group (ﬁg. 3). As has been reviewed in detail by Uher (2001), the exact values of y and z for the unique pnicogen position depend on the particular compound, and reﬂect the fact the pnicogen rings (ﬁg. 4) in the structure are not exactly square and the MX6 octahedra are slightly distorted. If the pnicogen rings were exactly square and the octahedra symmetric, the pnicogen position would reduce to (x = 0, y = 0.25, z = 0.25). The similarities between the ﬁlled skutterudite structure and the more familiar perovskite

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Fig. 2. Positional parameters for the pnicogen atoms of ﬁlled and unﬁlled skutterudites (ﬁgure from Kaiser and Jeitschko (1999)). The straight line indicates the condition for square pnicogen rings. In the ﬁgure T = Co, Rh or Ir; A = light lanthanides or Yb, Ca, Sr or Ba; R = light lanthanides.

Fig. 3. Model of the ﬁlled skutterudite structure. The transition metal atoms (Fe, Ru, or Os – small light blue spheres) are at the center of distorted octahedra formed by the pnicogen atoms (P, As, Sb – green spheres). The lanthanide atoms (red spheres) are located at the center of a cage formed by 12 pnicogen atoms. The skutterudite structure results if the lanthanide atoms are removed from the structure and the transition metals (Fe, Ru or Os) are replaced by transition metals with one more outer shell electron (Co, Rh or Ir).

(e.g., CaTiO3 ) and ReO3 structures have been discussed by Jeitschko and Braun (1977). In the ideal perovskite structure the eight octahedra are not tilted which results in eight voids that are ﬁlled by Ca atoms. The tilting of the octahedra in the skutterudite structure reduces the volume of six of these voids which become the centers of rectangular pnicogen (P4 , As4 or Sb4 ) groups. The remaining two voids are greatly enlarged and can accommodate lanthanide atoms (ﬁg. 4). Each lanthanide atom is located at the center of a distorted icosahedron formed by 12 pnicogen atoms. The size of this icosahedral cage formed by the pnicogen atoms increases as the pnicogen is changed from P to As to Sb. In many of the antimonide compounds the atomic displacement parameters for the lanthanide atoms are unusually large, indicating substantial “rattling” of the R atoms about their equilibrium positions and poor bonding to the antimony atoms forming the cage (Braun and Jeitschko, 1980a; Kaiser and Jeitschko, 1999). The ﬁlled skutterudite structure does not form with the smaller

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Fig. 4. Model of ﬁlled skutterudite structure that emphasizes the pnicogen-pnicogen bonding that results in nearly square pnicogen rings. The transition metal atoms (small white spheres) form a simple cubic lattice as shown. The lines connecting the transition metal atoms have been added for clarity and do not correspond to a chemical bond. The only chemical bonds shown in this model are those that form the pnicogen rings. The lanthanide atoms (large dark spheres) occupy the two voids without a pnicogen ring.

lanthanide elements (Dy–Tm) or Y or Sc because the pnicogen cage is too large for the necessary lanthanide-pnicogen bonding.

3. Lanthanide skutterudites as Zintl compounds The qualitative electronic structure of the ﬁlled skutterudites can be understood within the framework of the Zintl concept (for a good discussion of Zintl’s ideas see Corbett (1985), Muller (1993)). Zintl phases are characterized by the presence of covalently bonded anion structures similar to those found in the pure element. In the skutterudites, the pnicogen rings can be considered Zintl anions. The strongly electropositive cations (lanthanide elements and to a lesser extent the transition metal atoms), simply provide the necessary charge to complete the outer electron shell of the pnicogen anions. The Zintl concept can be applied to a huge number of compounds containing elements from the IVB, VB and VIB columns of the periodic table. Zintl compounds tend to be small gap semiconductors or bad metals. For the unﬁlled skutterudites, such as CoSb3 , each Sb atom is bonded to two Sb and two Co atoms, and each Co atom is bonded to six Sb atoms (ﬁgs. 3 and 4). The outer shell of each Sb atom is 5s2 p3 and so to attain a closed shell (5s2 p6 ) requires 3 electrons. The two covalent Sb–Sb bonds provide two of the electrons. The third electron is donated by the two Co atoms (a half an electron from each). This argument suggests that Co should have a formal valence of +3. In an octahedral site, the crystal ﬁeld will result in a splitting of the ﬁve Co 3d orbitals into a ground state triplet (t2g ) and an excited state doublet (eg ). (For an exceptionally clear discussion of why this occurs see Muller (1993).) The six d electrons of Co+3 can completely occupy the t2g orbital with no net magnetic moment, which is consistent with the measured diamagnetism for CoSb3 . This argument would also suggest that CoSb3 is a semiconductor. Although the simple Zintl concept appears to work for CoSb3 , it is important

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to realize that the Zintl picture is only a guideline and like many of the most useful guidelines they often work but sometimes they do not. In the case of CoSb3 it is not clear that the Zintl picture should work well since there is not much difference in electronegativity between Co (1.88) and Sb (2.05). Detailed electronic structure calculations (Singh and Pickett, 1994; Sofo and Mahan, 1998) indicate that the electronic structure of CoSb3 is rather complicated with a small gap of 0.05 eV at the Fermi energy due to a single band that crosses a much larger pseudogap (0.8 eV) between the valence and conduction bands. The electronic structure of the lanthanide ﬁlled skutterudites can also be analyzed using the Zintl picture. The lanthanide ﬁlled skutterudites (e.g., LaFe4 Sb12 ) form with the transition metals Fe, Ru or Os. These elements have one less outer electron relative to the elements in the next column of the periodic table (Co, Rh, or Ir). If the lanthanide elements contribute three electrons toward satisfying the bonding requirements of the pnicogen atoms, the total electron count is satisﬁed if each transition metal contributes on average 2.25 electrons. Although in terms of electron count an average valence of 2.25 should result in a semiconductor (within the Zintl picture), an average valence of 2.25 at each transition metal site would also imply a partially ﬁlled d band near the Fermi level. Since each transition metal is at a crystallographically equivalent site there is no reason to assume a spatial distribution of different transition metal valence states. This simple argument would suggest that the all of the lanthanide ﬁlled skutterudites should be poor metals. If the transition metal has an integer valence of +2, then a better metal should result with holes as the dominant carriers. For most of the lanthanide skutterudites the Zintl picture seems to be qualitatively correct at least as a starting point for understanding the electronic properties of these compounds. These simple ideas are useful but should only be regarded as guidelines and not a substitute for a modern electronic structure calculation. For example, density functional calculations of the electronic structure of CeFe4 Sb12 , and CeFe4 P12 indicate that both compounds are small band gap semiconductors (Nordstrom and Singh, 1996). The gap is due to strong hybridization between the Ce 4f level and Fe 3d and pnicogen states near the Fermi energy.

4. Synthesis and crystal growth The skutterudites do not melt congruently and involve pnicogens (P, As, Sb) that generally have high vapor pressures at the formation temperatures of the compounds. The high melting temperatures of Fe, Ru and Os coupled with the reactivity of the lanthanide metals with convenient crucible materials (e.g., SiO2 ) makes the synthesis of many of these compounds difﬁcult. As a result, variations in the reported properties of a particular lanthanide skutterudite compound can often be traced to differences in sample composition and quality. Small single crystals of most of the lanthanide phosphides can be grown in a molten tin ﬂux (Jeitschko and Braun, 1977; Meisner, 1981; Meisner et al., 1985; Delong and Meisner, 1985; Torikachvili et al., 1987; Watcharapasorn et al., 1999; Sato et al., 2000a, 2000b). For example, LaFe4 P12 crystals were grown using La ﬁlings, Fe powder, red phosphorus and Sn in the atomic ratio 1 : 4 : 20 : 50. The mixture was sealed in an evacuated silica tube, annealed for one week at 1050 K, and slow cooled (2 K/h) to about 773 K, followed by rapid cooling to room

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temperature. A 1 : 1 mixture of HCl and water was then used to dissolve the Sn ﬂux (Jeitschko and Braun, 1977). Single crystals with typical dimensions from 0.1 to 2 mm can be grown by this method. Although this recipe clearly works and has been used by several authors, it may not be the optimum procedure for growing the largest phosphide crystals based on the known binary phase diagrams. A larger concentration of Sn and a carbonized silica tube along with larger pieces of lanthanide metals and cooling to lower temperatures might result in larger phosphide crystals. Polycrystalline skutterudite phosphides have also been synthesized directly from the elements using a high pressure (4 GPa) and high temperature (800–1200 ◦ C) wedge-type cubic-anvil apparatus (Shirotani et al., 1996, 1997; Sekine et al., 1997; Uchiumi et al., 1999). This technique avoids contamination from residual Sn ﬂux. Lanthanide arsenides with the ﬁlled skutterudite structure were prepared by Braun and Jeitschko (1980b). Lanthanide arsenides, RAs, were ﬁrst prepared by reacting lanthanide ﬁlings with As in a silica tube at 900 K for two days. The RAs material was then ground together with the transition metal and excess As (R : T : As = 1 : 4 : 20) and sealed again in evacuated silica tubes, rapidly heated to 1150 K and kept at temperature for 3 h. The samples were then annealed at 1000 K for 4–7 days. The excess As was removed through sublimation. In spite of this elaborate synthesis procedure, the overall products were only 70–90% single phase. However, small single crystals of the skutterudite phase suitable for X-ray structure reﬁnement could often be isolated from the reaction product. A dense single phase sample of CeFe4 As12 was prepared by a similar procedure followed by the densiﬁcation of the powder with a hot-press (Watcharapasorn et al., 2002). Single phase arsenides with a variety of compositions have also been prepared via direct high-pressure high-temperature synthesis from the elements (Shirotani et al., 1997). Synthesis of the lanthanide antimonides with the ﬁlled skutterudite structure have been investigated in much more detail than either the arsenides or phosphides because of the excellent thermoelectric properties of these materials at elevated temperatures. These materials were ﬁrst synthesized by Braun and Jeitschko (1980a) using a procedure similar to that described above for the synthesis of the arsenides. The phase purity of the antimonides prepared in this manner was only about 80%. A better synthesis procedure was reported by Sales et al. (1996, 1997). A thin layer of carbon was deposited on the inside of a round-bottomed silica tube by the pyrolysis of acetone. Stoichiometric amounts of high purity lanthanide metal pieces (99.99% electropolished bar from Ames laboratory), Fe rod (99.9985% from Alfa Chemical Company), and Sb shot (99.999% from Alfa) were loaded into the precarbonized tube. The tube was sealed under vacuum at a pressure of 10−3 Pa and transferred into a programmable furnace. The silica ampoule was heated to 600 ◦ C at 2 ◦ C/min, left at 600 ◦ C for 3 h, and then slowly (0.5 ◦ C/min) heated to 1050 ◦ C and left for about 20–40 h. It is important to slowly heat the tube because of the highly exothermic reaction between the lanthanide elements (particularly Ce) and antimony. The silica ampoule containing the homogeneous molten liquid was removed from the furnace at temperature and quenched into a water bath. The same ampoule (containing the prereacted elements) was then placed in a furnace and annealed at 700 ◦ C for 30 h to form the correct crystallographic phase. The completely reacted solid was removed from the silica tube and cleaned with a wire brush to remove small amounts of carbon from the surface. To form a completely dense polycrys-

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talline solid, the reacted material was ball milled into a ﬁne powder in an argon atmosphere, loaded into a graphite die, and hot-pressed (5000 psi) in a helium atmosphere at 700 ◦ C for 40 min. This procedure results in single phase and dense polycrystalline samples suitable for further investigation (transport, magnetic, optical, etc.). Single crystals of the antimonides can also be grown using excess antimony as a ﬂux (Chakoumakos et al., 1999; Takeda and Ishikawa, 2000b; E.D. Bauer et al., 2001a, 2001b). High purity elements in the ratio R : T : Sb = 1 : 4 : 20 are loaded into an evacuated carbon coated quartz tube. The tubes are heated to 900 ◦ C for 24 h and then cooled slowly (1–3 ◦ C/h) to 600 ◦ C, followed by a quench to room temperature. The excess Sb ﬂux can be removed by etching in acid (HCl : HNO3 = 1 : 1). Small quantities of new compounds with the skutterudite structure can also be synthesized using a clever non-equilibrium thin ﬁlm method pioneered by D.C. Johnson and collaborators at the University of Oregon (Hornbostel et al., 1997a, 1997b). The new compounds are formed by the low-temperature interdiffusion of multilayer elemental reactants.

5. La ﬁlled skutterudites LaFe4 P12 is a metal that becomes superconducting for temperatures below 4.1 K (Meisner, 1981). The residual resistance ratio (RRR) for these crystals is large RRR = 90–1500 indicating good crystallographic perfection (Torikachvili et al., 1987; Sato et al., 2000a, 2000b; Sugawara et al., 2000). The resistivity at room temperature is about 250 μ cm (Sugawara et al., 2000) in fair agreement with optical conductivity data which yields a value of 85 μ cm (Dordevic et al., 1999). Superconductivity is rare in compounds that contain such high concentrations of iron. Mössbauer measurements found that each iron atom in LaFe4 P12 carried a magnetic moment less than 0.01μB (Shenoy et al., 1982; Grandjean et al., 1984). The magnetic susceptibility data is weakly temperature dependent and saturates below 50 K at a value of 8 × 10−4 cm3 /mol (emu/mol) (Meisner, 1981; Grandjean et al., 1984). If the iron moments are in a low spin conﬁguration similar to Fe+2 , from the Zintl picture discussed in sect. 3, the compound should be a hole doped metal. Hall measurements (Sato et al., 2000b) and band structure calculations (Harima, 1998, 2000) both indicate hole like conduction. Band structure predicts two hole-like Fermi sheets, a nearly spherical sheet composed mainly of Fe 3d states and a multiply connected sheet of mainly P–p character (ﬁg. 5). The band structure calculations are in good agreement with the two masses extracted from dHvA measurements on LaFe4 P12 crystals (Sugawara et al., 2000). The predicted electronic speciﬁc heat coefﬁcient, γ , from the band structure calculations, was 32 mJ/mol K2 in fair agreement with the experimental value of 57 mJ/mol K2 (Torikachvili et al., 1987). The relatively high density of electronic states and the absence of magnetism suggests that LaFe4 P12 is a relatively normal BCS superconductor. The jump in the heat capacity at Tc = 4.1 K is about 87% of the value expected from BCS theory. LaRu4 P12 is a metal that superconducts below 7.2 K (Meisner, 1981; Delong and Meisner, 1985; Uchiumi et al., 1999). The room temperature resistivity of a polycrystalline sample was 600 μ cm decreasing to about 20 μ cm at 8 K (Shirotani et al., 1996). Analysis of the low

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(a)

9

(b)

Fig. 5. The Fermi surface of LaFe4 P12 consists of two hole-like Fermi sheets. The ﬁrst sheet (a) is nearly spherical with mainly Fe 3d character while the second sheet (b) is multiply connected with mainly P–p character. Both surfaces are centered at the Γ point. Various high-symmetry directions are noted in (a) (Harima, 1998; Sugawara et al., 2000).

temperature heat capacity data yields γ = 26 mJ/mol K2 and a Debye temperature, ΘD = 446 K. The magnetic susceptibility is essentially temperature independent from 7–300 K, consistent with Pauli paramagnetism (Uchiumi et al., 1999). LaOs4 P12 is a metal with a room temperature resistivity of about 400 μ cm, which decreases to 50 μ cm at 2 K followed by superconductivity at 1.8 K (Shirotani et al., 1996; Meisner, 1981). There is a weak decrease of Tc with increasing pressure (Delong and Meisner, 1985). LaFe4 As12 is a metal that shows a monotonic decrease in resistivity down to 2 K with no evidence of superconductivity (Shirotani et al., 2000). LaRu4 As12 is a poor metal with the highest superconducting transition temperature (10.3 K) of all of the ﬁlled skutterudites. Polycrystalline samples can be prepared using high pressure and high temperature (Shirotani et al., 1996, 1997, 2000; Uchiumi et al., 1999). The resistivity at room temperature is 13 m cm decreasing to 3 m cm at 12 K. The temperature dependence of the resistivity exhibits a large positive curvature that suggests substantial structure in the electronic density of state near the Fermi energy. Low temperature heat capacity measurements yield γ = 73 mJ/mol K2 , and ΘD = 233 K. The normalized jump in the heat capacity at Tc is 1.75 which is slightly larger than the BCS value of 1.43. With increasing pressure Tc decreases at the rate dTc /dP = −0.4 K/GPa (ﬁg. 6). LaOs4 As12 is metallic exhibiting superconductivity below 3.2 K (Shirotani et al., 2000). The resistivity (polycrystalline sample) at room temperature is 0.8 m cm decreasing to 0.1 m cm at 4 K. LaFe4 Sb12 is a poor metal or heavily doped semiconductor with good thermoelectric properties above room temperature (700–1000 K) (Sales et al., 1996, 1997). Only polycrystalline samples have been investigated. The room temperature resistivity is about 0.5 m cm de-

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Fig. 6. Electrical resistivity of LaRu4 As12 vs. temperature and pressure (Shirotani et al., 2000).

Fig. 7. Seebeck coefﬁcient vs. temperature for LaFe4 Sb12 and CeFe4 Sb12 (Sales et al., 1997, unpublished).

creasing to 0.1 m cm at 10 K. The typical carrier concentration estimated from room temperature Hall data is 2 × 1021 holes/cm3. The Seebeck coefﬁcient, S, at room temperature is +75 μV/K which is typical for a heavily doped semiconductor (the value of S for a good metal is usually less than 10 μV/K in magnitude). The electronic structure near the Fermi energy has more that one type of band since the Seebeck coefﬁcient changes sign near 100 K (ﬁg. 7). There has been no report of superconductivity in this material above 2 K. There is no evidence of long range magnetic order. The magnetic susceptibility indicates some type of enhanced paramagnetism that is probably associated with nearly itinerant 3d electrons (Ravot et al., 2001; Dannebrock et al., 1996; Sales, unpublished). Although the temperature dependence of the susceptibility is similar for all three samples, the magnitude of the room temperature susceptibility varies substantially from 0.0019 emu/mol (Ravot et al., 2001) to 0.004 (Dannebrock et al., 1996) – note that all of the susceptibility data in Dannebrock’s ﬁg. 2 appears

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to be mislabeled since the susceptibility values are too high by a factor of 10). At helium temperatures the susceptibility saturates for all three samples near 0.02 emu/mol. Probably the best interpretation of the susceptibility data was given by Ravot et al. (2001) who were able to account for the nearly Curie–Weiss dependence of the susceptibility in terms of a Stoner band picture. This interpretation is also consistent with the discussion in sect. 3, which implies some type of band magnetism if the average iron valence is 2.25. However, the signiﬁcant variation of the susceptibility from sample to sample and the difﬁculty in ruling out small amounts (< 3%) of a magnetic impurity phase suggests that the magnetism may not be intrinsic to the skutterudite phase. Susceptibility measurements should be repeated using a single crystal free of impurity phases. Braun and Jeitschko (1980a) noted that the lanthanide site in the antimonides is too large for La, the largest trivalent lanthanide element. The poor bonding of La to the surrounding antimony atoms results in a large atomic displacement parameter (ADP) for La and corresponds to the La “rattling” about its equilibrium position. As a ﬁrst approximation the rattling La atom can be treated as a localized Einstein oscillator. Slack (1995) was ﬁrst to suggest that if the frequency of the Einstein oscillator is low enough, it could result in a substantial reduction in the lattice thermal conductivity of the ﬁlled skutterudites by hybridizing with the acoustic phonons that carry the majority of the heat in most solids. This idea has been experimentally veriﬁed by many authors (Morelli and Meisner, 1995; Sales et al., 1996, 1997, 2000, 2001a, 2001b; Fleurial et al., 1996; Nolas et al., 1996a, 1996b, 1998; Morelli et al., 1997; Meisner et al., 1998). A low lattice thermal conductivity, κL , is necessary for a good thermoelectric material. The room temperature value of κL for dense polycrystalline LaFe4 Sb12 is approximately 1.5 W/mK. An estimate of the Einstein frequency for La in LaFe4 Sb12 has been obtained from heat capacity, elastic constant, inelastic neutron scattering (ﬁg. 8), ADP data and theory (Sales et al., 1997, 1999; Keppens et al., 1998; Feldman et al., 2000). All of the measurements indicate a characteristic Einstein temperature of about 75 K for the La atoms.

Fig. 8. Difference in the inelastic neutron scattering data between LaFe4 Sb12 and CeFe4 Sb12 vs. energy loss (Keppens et al., 1998). CeFe4 Sb12 was used as a reference compound since the neutron scattering cross section of Ce is much smaller than that of La. The difference spectra therefore reﬂect the vibrational density of states (DOS) associated with the La atoms. The peak at 7 meV (78 K) corresponds to the quasi-localized La mode. The second broader peak at about 15 meV corresponds to the hybridization of La and Sb vibrational modes. Both peaks can be accounted for using lattice dynamic models based on ﬁrst-principles calculations (Feldman et al., 2000).

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LaRu4 Sb12 is metallic and is superconducting below about 3.6 K (Uchiumi et al., 1999; Takeda and Ishikawa, 2000b; E.D. Bauer et al., 2001a). Low temperature heat capacity data yield γ = 37 mJ/mol K2 and ΘD = 253 K. The residual resistivity ratio (RRR) is about 69 for the small crystals but no absolute values for the resistivity are reported (Takeda and Ishikawa, 2000b). Polycrystalline samples synthesized at high pressures have a resistivity of 0.7 m cm and a much smaller RRR of 7. The Tc of the polycrystalline material is also signiﬁcantly lower (2.8 K) (Uchiumi et al., 1999). The normalized jump in the heat capacity at Tc is 2.22, which suggests that LaRu4 Sb12 is a superconductor with moderate coupling (Takeda and Ishikawa, 2000b). The room temperature magnetic susceptibility of LaRu4 Sb12 is diamagnetic with a value of −1.93 × 10−4 emu/mol. LaOs4Sb12 is presumably a metal although only heat capacity data from small single crystals have been published resulting in γ = 36 mJ/mol K2 and ΘD = 304 K. There is no evidence for superconductivity above 0.5 K (E.D. Bauer et al., 2001b).

6. Ce ﬁlled skutterudites CeFe4 P12 is a small gap semiconductor with the gap likely arising from the hybridization of the Ce 4f states with the Fe 3d and 5b–p states in the vicinity of the Fermi energy (Meisner et al., 1985; Nordstrom and Singh, 1996). The susceptibility of CeFe4 P12 is small (2.6 × 10−4 emu/mol), and is roughly a factor of 2 less than its non-magnetic analog LaFe4 P12 . The lattice constant of CeFe4 P12 (7.792 Å) is signiﬁcantly smaller than would be expected for trivalent Ce based on the values for LaFe4 P12 (7.8316 Å) and PrFe4 P12 (7.8149 Å). The susceptibility data and the lattice constant suggest the possibility of Ce+4 . However, XANES (X-ray absorption near edge spectroscopy) measurements (Xue et al., 1994) clearly indicate that the Ce is primarily trivalent, though with some evidence of complex electronic behavior. The resistivity increases with decreasing temperature but the behavior is complicated and somewhat sample dependent (Meisner et al., 1985; Sato et al., 2000b). Analysis of single crystal resistivity data above 250 K gives a transport gap of about 0.12 eV (Sato et al., 2000b) which is close to the value of 0.15 eV measured from infrared reﬂectance spectroscopy (Dordevic et al., 1999). Both values are somewhat smaller than the value of 0.34 eV calculated within the local-density approximation (LDA) (Nordstrom and Singh, 1996). The temperature dependence of the Hall coefﬁcient from 2–300 K appears to be reproducible from crystal to crystal but is difﬁcult to interpret (Sato et al., 2000b). The Seebeck coefﬁcient at room temperature is large for single crystals (≈ 0.5 mV/K) (Sato et al., 2000b) but is about 10 times smaller in hot-pressed polycrystalline samples with small amounts of impurity phases (Watcharapasorn et al., 1999). The room temperature thermal conductivity of a polycrystalline sample is 14 W/m K, which is about ten times larger than the typical values of good thermoelectric materials (Watcharapasorn et al., 1999). CeRu4 P12 is a narrow gap semiconductor with a gap of 0.075 eV estimated from electrical transport measurements on polycrystalline samples (Shirotani et al., 1996). XANES measurements indicate trivalent Ce with strong hybridization with ligand orbitals. The gap is presumably formed from the hybridization of the Ce 4f states with the Ru d and P–p orbitals

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(Kanai et al., 2002). The room temperature thermal conductivity of a dense polycrystalline sample is 8.6 W/m K (Watcharapasorn et al., 1999). The magnetic susceptibility is paramagnetic but relatively small at room temperature (≈ 0.001 cm3 /mol Ce) and increases to about 0.018 cm3 /mol at 2 K (Shirotani et al., 1999). These values indicate a substantial reduction in the magnetism of the Ce 4f shell due to hybridization. CeOs4 P12 is a narrow gap semiconductor with a gap of ≈ 0.036 eV (≈ 400 K) estimated from resistivity data (Shirotani et al., 1999). The room temperature resistivity is ≈ 10−2 cm increasing to ≈ 104 cm at 2 K. The magnetic susceptibility is similar to that of CeRu4 P12 (Shirotani et al., 1999). The as-grown samples are p-type with a room temperature Hall mobility of 73 cm2 /V s for a carrier concentration of 5 × 1019 cm−3 . The room temperature values of the Seebeck coefﬁcient and thermal conductivity are +147 μV/K and 10.5 W/m K, respectively (Sekine et al., 2001). CeFe4 As12 is probably a narrow gap semiconductor, but little low temperature data are available for this compound. The resistivity of a polycrystalline sample indicates a small gap on the order of 0.01 eV (Grandjean et al., 1984). The high temperature thermoelectric properties of this compound were investigated by Watcharapasorn et al. (2002). They found semimetallic behavior with a room temperature resistivity of 0.49 m cm, a Seebeck coefﬁcient of 40 μV/K, and a thermal conductivity of 3.8 W/m K. The maximum value for ZT, the thermoelectric ﬁgure of merit, was estimated to be 0.4 at 850 K. CeRu4 As12 – only crystallography data has been reported for this compound (see table 1). CeFe4 Sb12 is a moderately heavy fermion metal at low temperatures (Morelli and Meisner, 1995; Gajewski et al., 1998; E.D. Bauer et al., 2000) and has excellent thermoelectric properties at elevated temperatures (Sales et al., 1996, 1997; Fleurial et al., 1996). LDA calculations predict a small gap (0.1 eV) that is not observed experimentally (Nordstrom and Singh, 1996). The hybridization between the Ce 4f and the Fe 3d and Sb–p states at the Fermi energy is apparently not large enough to create a gap. XANES measurements (Grandjean et al., 2000) indicate a Ce valence of 3 ± 0.02, and iron Mössbauer data show no indication of magnetic order (Long et al., 1999). All of the reported data are from polycrystalline samples. Analysis of the low temperature heat capacity and magnetization data are complicated by small amounts of impurity phases (Morelli and Meisner, 1995; Chen et al., 1997; Gajewski et al., 1998). Analysis of the low temperature heat capacity data yields γ = 180 mJ/mol K2 and ΘD ≈ 250 K (Gajewski et al., 1998). The resistivity of CeFe4 Sb12 has an unusual “S” shape that is characteristic of many concentrated Kondo compounds (ﬁg. 9b). The rapid decrease in resistivity at about 100 K is caused by the coherent scattering of electrons from the lanthanide sublattice. The interpretation of the magnetic data is complicated by an enhanced Pauli contribution from the Fe (Ravot et al., 2001), a relatively high Kondo temperature, TK , of about 100 K (Gajewski et al., 1998) and the crystal ﬁeld splitting of the Ce 4f level in a cubic crystal ﬁeld. In spite of these complications, it is clear that the value of the Wilson–Sommerfeld ratio Rw = (χ0 /γ )(π 2 kB2 /μ2eff ) is of the order unity as expected for heavy fermion systems (Wilson, 1975). In the expression for Rw , χ0 is the extrapolated Pauli susceptibility at T = 0 (0.008 emu/mol Ce), and μeff is the magnetic moment per Ce ion (2.54μB ).

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B.C. SALES Table 1 Crystallography data and ground state properties of ﬁlled skutteruditesa

LaFe4 P12 LaRu4 P12 LaOs4 P12 LaFe4 As12 LaRu4 As12 LaOs4 As12 LaFe4 Sb12 LaRu4 Sb12 LaOs4 Sb12

Lattice constant (Å) 7.8316 8.0561 8.0844 8.3252 8.5081 8.5437 9.1395 9.2700 9.3029

Density (g/cm3 ) (X-ray density) 5.08 5.81 7.99 7.26 7.77 9.57 7.93 8.35 9.74

CeFe4 P12 CeRu4 P12 CeOs4 P12 CeFe4 As12 CeRu4 As12 CeOs4 As12 CeFe4 Sb12 CeRu4 Sb12 CeOs4 Sb12

7.7920 8.0376 8.0626 8.2959 8.4908 8.5249 9.1350 9.2657 9.3011

PrFe4 P12 PrRu4 P12 PrOs4 P12 PrFe4 As12 PrRu4 As12 PrOs4 As12 PrFe4 Sb12 PrRu4 Sb12 PrOs4 Sb12

Compound

Ground state/transition temperature (K) S, Tc = 4.1 S, Tc = 7.2 S, Tc = 1.8 M S, Tc = 10.3 S, Tc = 3.2 M S, Tc = 2.8 M

1 1 1 3 3 3 2 2 2

5.16 5.86 8.06 7.34 7.83 9.64 7.95 8.37 9.75

HGS HGS HGS – – – HFM NFL, QCP HGS

1 1 1 3 3 3 2 2 2

7.8149 8.0420 8.0710 8.3125 8.4963 8.5311 9.1351 9.2648 9.2994

5.12 5.86 8.04 7.30 7.82 9.62 7.95 8.38 9.76

QO, TQO = 6.5, FIHFM M-I, TM-I = 60, TAF ≈ 0.3 M – S, Tc = 2.4 – FMM, TFM = 5

1 1 1 3 3 3 2 2 2

NdFe4 P12 NdRu4 P12 NdOs4 P12 NdFe4 As12 NdRu4 As12 NdOs4 As12 NdFe4 Sb12 NdRu4 Sb12 NdOs4 Sb12

7.8079 8.0364 8.0638 8.309 – 8.5291 9.130 9.2642 9.2989

5.16 5.89 8.09 7.39

1 1 1 9

9.65 8.04 8.39 9.77

FMM, TFM = 5 FMM, TFM = 1.5 – – – – – AFM?, TAF = 1.3 Td = 187

SmFe4 P12 SmRu4 P12 SmFe4 Sb12 SmRu4 Sb12 SmOs4 Sb12

7.8029 8.0397 9.130 9.259 9.3009

5.21 5.96 8.06 8.49 9.79

M M-I & TAF = 16 FMM, TFM = 45 – –

1 11 5 5 2

EuFe4 P12 EuRu4 P12

7.8055 8.0406

5.22 5.93

FMM, TFM = 100 1 FMM, TFM = 18 1 continued on next page

HFSC, Tsc = 1.8

Ref.

3 5 2 2

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Table 1, continued

EuFe4 Sb12 EuRu4 Sb12 EuOs4 Sb12

Lattice constant (Å) 9.165 9.2824 9.3187

Density (g/cm3 ) (X-ray density) 7.98 8.42 9.74

GdFe4 P12 GdRu4 P12

7.795 8.0375

TbRu4 P12

Compound

Ground state/transition temperature (K) FMM, TFM = 84 FMM, TFM = 3.3 –

Ref. 5 2 2

5.31 6.01

FMM, TFM = 22 AFM?, TAF = 21

9 11

8.0338

6.03

AFM?, TAF = 20, 10

11

YbFe4 Sb12 YbOs4 Sb12

9.1580 9.316

8.09 9.91

HFM, Mixed Valence

7 6

ThFe4 P12 ThRu4 P12 ThOs4 As12

7.7999 8.0461 8.5183

5.83 6.47 10.24

4 4 4

UFe4 P12 CaFe4 Sb12

7.7709 9.162

5.94 7.5

5 5

SrFe4 Sb12 SrRu4 Sb12 SrOs4 Sb12

9.1782 9.2891 9.322

7.67 8.15 9.52

10 5 10

BaFe4 Sb12 BaRu4 Sb12 BaOs4 Sb12

9.200 9.315 9.3401

7.82 8.29 9.68

8 5 10

a Symbols:

S, superconductor; HGS, hybridization gap semiconductor; HFM, heavy fermion metal; M, metallic; NFL, non-Fermi liquid; QCP, quantum critical point; QO, quadrupolar order;

FIHFM, ﬁeld-induced heavy-fermion metal; FMM, ferromagnetic metal; AFM, antiferromagnetic metal; M-I, metal to insulator transition; AFM?, unusual magnetic phase transition; Td , displacive transition.

References 1. Jeitschko and Braun (1977) 2. Braun and Jeitschko (1980a) 3. Braun and Jeitschko (1980b) 4. Braun and Jeitschko (1980c)

5. Evers et al. (1995) 6. Kaiser and Jeitschko (1999) 7. Dilley et al. (1998) 8. Stetson et al. (1991)

9. Jeitschko et al. (2000) 10. Evers et al. (1994) 11. Sekine et al. (2000a)

CeRu4 Sb12 is an unusual metal that exhibits non-Fermi liquid (NFL) behavior in the low temperature speciﬁc heat, resistivity, and magnetic susceptibility measurements on single crystals (Takeda and Ishikawa, 2000a, 2000b, 2001; E.D. Bauer et al., 2001a). CeRu4 Sb12 may be near a ferromagnetic quantum critical point. The low temperature (T < 4 K) speciﬁc heat (ﬁg. 10) and magnetic susceptibility of CeRu4 Sb12 are well described by a logarithmic divergence or a power law in temperature. The characteristic temperature, T ∗ , that is associated with the maximum in the magnetic susceptibility and with the rapid drop in the

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Fig. 9. (a) Scaled resistivity ρ(T )/ρ (300 K) vs. T /T0 for YbFe4 Sb12 , where T0 is the scaling temperature. Inset shows the pressure dependence of T0 . (b) Scaled resistivity of CeFe4 Sb12 vs. T /T0 . Inset shows pressure dependence of T0 . The room temperature resistivity of both compounds was about 0.8 m cm at ambient pressure (E.D. Bauer et al., 2000).

Fig. 10. Electronic contribution to the heat capacity divided by temperature vs. log10 T for a series of La doped alloys of CeRu4 Sb12 . The data has been corrected for a phonon contribution, using heat capacity data from LaRu4 Sb12 , and a nuclear quadrupolar contribution from 121 Sb and 123 Sb (Takeda and Ishikawa, 2001).

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resistivity is about 75 K. The low temperature carrier mass, m∗ , estimated from heat capacity and optical studies, is about 85 times the free electron mass (Dordevic et al., 2001). Optical measurements are able to directly measure the pseudo-gap, Δ, created by the hybridization between the Ce 4f states and the extended conduction band states. The mass enhancement scales as m∗ /me = (Δ/T ∗ )2 as predicted by theory (Millis et al., 1987). The low temperature resistivity data for CeRu4 Sb12 reported by Takeda and Ishikawa (2000a, 2000b, 2001) follows a power law in temperature (ραT n ) with n = 1.65. A magnetic ﬁeld greater than 2 T appears to restore Fermi liquid behavior (n = 2) for temperatures less than 1 K, as did the substitution of a small amount of La for Ce. The La-doping studies suggest that the parent compound, CeRu4 Sb12 , is near a ferromagnetic quantum critical point. In contrast, E.D. Bauer et al. (2001a) found that the electrical resistivity is sample dependent with some specimens exhibiting NFL behavior below 5 K. For these samples the application of magnetic ﬁelds up to H = 8 T does not signiﬁcantly change the non-Fermi liquid ground state. The low temperature transport properties of CeRu4 Sb12 crystals are clearly sensitive to small changes in composition or small concentrations of impurities in the starting materials. CeOs4 Sb12 is a narrow gap semiconductor with the gap caused by the hybridization of the Ce 4f level with states near the Fermi energy. Transport data on small single crystals shows a weakly activated behavior corresponding to a gap of about 10 K (E.D. Bauer et al., 2001b). Heat capacity data give γ ≈ 92 mJ/mol K2 and ΘD = 304 K. No magnetic order was found above 0.5 K. The temperature dependence of the magnetic susceptibility data suggests a relatively large crystalline electric ﬁeld splitting (327 K) of the Ce 4f level.

7. Pr ﬁlled skutterudites PrFe4 P12 is quite an unusual compound that exhibits weak semiconducting behavior from 20–300 K followed by an even stranger phase transition near 5 K (ﬁg. 11) (Sato et al., 2000a, 2000b; Aoki et al., 2002). Originally it was thought that the low temperature phase transition corresponded to the onset of antiferromagnetic ordering of the Pr magnetic moments (Torikachvili et al., 1987). More recent work indicates that the phase transition probably corresponds to the ordering of the Pr quadrupole moments since for temperatures below the transition each Pr ion has a low magnetic moment implying a non-magnetic ground state (< 0.03μB /Pr) (Aoki et al., 2002). No magnetic ordering is evident in neutron scattering measurements (Keller et al., 2001). The Hall coefﬁcient changes by more than two orders of magnitude below 5 K but becomes temperature independent below 2 K. The Hall data suggests a gap structure similar to that seen in the resistivity (ﬁg. 11) and heat capacity data. The Seebeck coefﬁcient is extremely large below 5 K reaching a maximum value of −130 μV/K at 4 K, which reﬂects an unusually sharp feature in the electronic density of states. The application of a magnetic ﬁeld induces a transition to a heavy-fermion state (HFS) with a well-deﬁned phase boundary as a function of magnetic ﬁeld and temperature (ﬁgs. 12, 13). A metamagnetic phase transition (ﬁg. 14) is also associated with the phase boundary (Torikachvili et al., 1987; Matsuda et al., 2000; Aoki et al., 2002). It is suggested that the quadrupolar degrees of freedom are essential for the formation of the heavy-fermion state in this material. The crystalline

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Fig. 11. Electrical resistivity vs. log10 T for PrFe4 P12 . Below 3 K the resistivity is accurately described by ρ(T ) = 20 + 273T 2 exp(−6.8/T ), corresponding to the temperature dependence of scattering with a gap structure (Sato et al., 2000a).

Fig. 12. Total heat capacity of a single crystal of PrFe4 P12 vs. temperature in various applied magnetic ﬁelds: (a) low ﬁelds and (b) high ﬁelds. The dashed lines in (b) correspond to the best ﬁt of the heavy fermion state to the resonant level model (CRLM ). Cph is the estimate of the phonon contribution to the heat capacity (Aoki et al., 2002).

electric ﬁeld level schemes estimated from the anisotropy in the magnetization are consistent with this conjecture. The de Haas–van Alphen (dHvA) effect has been used to study the electronic structure of PrFe4 P12 . An enormously enhanced cyclotron effective mass of 81 me was found in the HFS phase. In the low ﬁeld ordered phase a dHvA branch with a mass of 10 me was also observed (Sugawara et al., 2001).

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Fig. 13. Magnetic ﬁeld vs. temperature phase diagram of single crystal PrFe4 P12 with the magnetic ﬁelds applied along the (100) direction. The labels ODS and HFS refer to ordered state and heavy fermion state, respectively. The ordered state is probably due to quadrupolar ordering of the Pr 4f ground state. The solid and broken lines represent second-order and ﬁrst-order phase boundaries, respectively (Aoki et al., 2002).

Fig. 14. Magnetization vs. ﬁeld at 2.5, 4.2 and 7 K with the magnetic ﬁeld applied along the main symmetry directions of PrFe4 P12 . The observed magnetic anisotropy is a feature of the non-ordered state (Aoki et al., 2002).

PrRu4 P12 exhibits an unusual metal–insulator transition (M-I) at about 60 K (ﬁg. 15) (Sekine et al., 1997). There is no magnetic anomaly associated with this transition and originally it was thought there is no structural change associated with the M-I. A small struc-

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Fig. 15. Normalized resistivity of PrRu4 P12 vs. temperature at pressures from 1 atm to 1.6 GPa (Sekine et al., 1997).

tural transition was subsequently detected using electron diffraction in which the space group changes from Im3 (the skutterudite space group) to probably Pm3 (Lee et al., 2001). XANES measurements give a Pr valence of +3 for temperatures between 20 and 300 K, suggesting that there is no valence transition associated with the M-I (Lee et al., 1999). The opening of a gap at the Fermi energy (Nanba et al., 1999) is either due to a small displacement of the P atoms in the structure or perhaps charge ordering on the phosphorus (Lee et al., 2001). For temperatures near 60 K, Raman measurements on PrRu4 P12 indicate the softening of a mode at 380 cm−1 that is associated with P vibrations (Sekine et al., 1999). There is a small jump in the thermal expansion coefﬁcient at 63 K (≈ 5 × 10−7 K−1 ) that shows no evidence of thermal hysteresis, indicating a second order phase transition. The thermal expansion anomaly is unaffected in magnetic ﬁelds up to at least 7 T (Matsuhira et al., 2000). The magnetic susceptibility data follow a Curie–Weiss law at high temperatures with an effective moment of 3.8μB and a Weiss temperature of −7 K. The low temperature susceptibility (< 100 K) is complicated by the crystalline electric ﬁeld at the Pr site that splits the J = 4 4f level (Sekine et al., 1997, 2000c). Heat capacity data suggest that the ground state of the Pr 4f shell is a Γ3 non-Kramers doublet. Antiferromagnetic order likely occurs for T < 0.35 K (Meisner, 1981). PrOs4 P12 is a metallic with a relatively temperature independent resistivity for temperatures between 50 and 300 K. Below 50 K there is a rapid drop in the resistivity similar to that observed in Pr metal or Kondo lattice Ce compounds such as CeFe4 Sb12 (ﬁg. 9). There is also a small kink in the resistivity at 7 K of unknown origin. The magnetic susceptibility

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data follows a Curie–Weiss law at high temperatures with an effective moment of 3.63μB and a Weiss temperature of −17 K. There is no evidence for magnetic order above 1 K. Magnetization measurements at 2 K indicate a non-magnetic ground state caused by the crystalline electric ﬁeld (Sekine et al., 1997). PrFe4 As12 – only crystallography data have been reported for this compound (see table 1). PrRu4 As12 is a superconductor below 2.4 K. The resistivity of a polycrystalline sample changes from 1 m cm at room temperature to 0.25 m cm at 3 K (Shirotani et al., 1997). PrOs4 As12 – only crystallography data have been reported for this compound (see table 1). PrFe4 Sb12 is likely a metal. Magnetic measurements on polycrystalline samples that were about 90% phase pure indicated ferromagnetic ordering below 5 K with a moment of 1μB per formula unit. The only other phase detected using X-ray diffraction was FeSb2 , which has a weak Pauli paramagnetic susceptibility (Dannebrock et al., 1996). PrRu4 Sb12 is a metal that becomes superconducting below 1 K. Heat capacity data conﬁrm the bulk nature of the superconductivity with ΔC/γ Tc = 1.87, which is larger than the 1.43 value expected from BCS theory. Values for ΘD and γ are 232 K and 59 mJ/mol K2 , respectively. The magnetic susceptibility data indicates a non-magnetic ground state for the Pr +3 ions and a substantial crystal ﬁeld splitting greater than 125 K (Takeda and Ishikawa, 2000b).

Fig. 16. (a) Resistivity and magnetic susceptibility, and (b) heat capacity data for PrOs4 Sb12 (E.D. Bauer et al., 2002).

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PrOs4 Sb12 is the ﬁrst known example of a heavy-fermion superconductor containing Pr (E.D. Bauer et al., 2002). Heavy-fermion behavior is inferred by the size of the jump in the heat capacity at Tc = 1.76 K and by the slope of the critical ﬁeld near Tc . Both analyses suggest γ ≈ 350 mJ/mol K2 and m∗ ≈ 100 me . The resistivity, magnetic susceptibility and heat capacity data are shown in ﬁg. 16. The analysis of the data is complicated by the crystal electric ﬁeld (CEF) splitting of the Pr levels 4f levels. The resistivity drops by almost a factor of 2 between 7 K and the onset of the superconducting transition at 1.76 K. In many lanthanide compounds this drop is often indicative of low lying CEF levels. The broad Schottky like peak at 2.2 K is also consistent with this hypothesis. Quantitative ﬁts to the magnetic susceptibility data plus an analysis of inelastic neutron scattering (Maple et al., 2002) and heat capacity data imply the J = 4 Pr+3 level is split into a non-magnetic Γ3 doublet ground state, a Γ5 triplet at 8.2 K, a Γ4 triplet at 133 K and a Γ1 singlet at 320 K above the ground state. Heavy fermion behavior likely arises in this compound due to the interaction between the charge on the conduction electrons and ﬂuctuations of the Pr+3 electric quadrupole moments associated with the Γ3 doublet ground state. The effect of Pr+3 quadrupole ﬂuctuations on the superconductivity of PrOs4 Sb12 is an open question.

8. Nd ﬁlled skutterudites NdFe4 P12 is metallic and orders ferromagnetically below 2 K (Torikachvili et al., 1987). The resistivity decreases monotonically from a value of ≈ 150 μ cm at room temperature to ≈ 25 μ cm at 30 K. Below 30 K the resistivity increases with decreasing temperature (ﬁg. 17) until the ferromagnetic phase transition is reached at 2 K. Below this transition the resistivity decreases as T 4 , rather than the T 2 expected from magnon scattering (Sato et al., 2000a, 2000b). The heat capacity data below 2 K decreases as T 3 rather than the T 3/2 expected for a simple ferromagnet (Torikachvili et al., 1987). Both the heat capacity data and the resistivity

Fig. 17. Low temperature resistivity data for NdFe4 P12 (Sato et al., 2000b).

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can be understood if the magnon energy is linear in wavevector k rather than proportional to k 2 (Sato et al., 2000a, 2000b). The magnetic susceptibility follows a Curie–Weiss law for temperatures between 180 and 300 K with an effective moment of 3.53μB , close to the Nd+3 free ion value of 3.62μB . Below 150 K the positive curvature in the susceptibility indicates the effects of the CEF. Neutron scattering measurements have conﬁrmed the ferromagnetic ordering of the Nd moments below 2 K (Keller et al., 2001). The ordered moment was found to be 1.6μB at 1.5 K. De Hass–van Alfen measurements on NdFe4 P12 crystals showed a Fermi surface similar to LaFe4 P12 except for the splitting of the dHvA branches due to the ferromagnetic exchange interaction (Sugawara et al., 2000). NdRu4 P12 is a metal that becomes ferromagnetic below 1.5 K (Sekine et al., 1998). Room temperature Raman data have been reported for this compound (Sekine et al., 1998). Three distinct Raman modes at 370, 385, and 415 cm−1 were observed, but there was no detailed analysis of exactly which vibrations should be associated with these modes. NdOs4 P12 – only crystallography data have been reported for this compound (see table 1). NdFe4 As12 – only crystallography data have been reported for this compound (see table 1). NdRu4 As12 – has not been synthesized. NdOs4 As12 – only crystallography data have been reported for this compound (see table 1). NdFe4 Sb12 – only crystallography data have been reported for this compound (see table 1). NdRu4 Sb12 is metallic and undergoes some type of magnetic transition near 1.3 K. The magnetic susceptibility follows a Curie–Weiss law above 50 K with an effective moment of 3.45μB and a Weiss temperature of −28 K. Crystal ﬁelds likely effect the susceptibility and magnetic interactions for temperatures below 50 K. Low temperature heat capacity data conﬁrm the bulk nature of the magnetic transition (Takeda and Ishikawa, 2000b). NdOs4 Sb12 may undergo a displacive-type phase transition at −86 ◦ C in which the Nd atoms freeze at off center positions (Evers et al., 1995). This transition was proposed on the basis of scanning calorimetry measurements and the huge room temperature value for the Nd atomic displacement parameter (Beq = 4 Å2 ). 9. Sm ﬁlled skutterudites SmFe4 P12 is a metal that shows Van Vleck paramagnetism (Jeitschko et al., 2000). SmRu4 P12 undergoes a metal to insulator transition in conjunction with antiferromagnetic ordering at 16 K (Sekine et al., 1998). SmFe4 Sb12 is metallic and orders ferromagnetically for temperatures below 45 K with a relatively small saturation moment of 0.7μB (Dannebrock et al., 1996). SmRu4 Sb12 and SmOs4 Sb12 – only crystallography data have been reported for these compounds (see table 1). 10. Eu ﬁlled skutterudites EuFe4P12 is metallic and orders ferromagnetically for temperatures below 100 K (Grandjean et al., 1984). The effective moment, as determined from the high temperature magnetic sus-

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ceptibility data, is 6.2μB per formula unit which is lower than the value expected for Eu+2 of 7.94μB . The hyperﬁne parameters as determined from Mössbauer spectroscopy are unusual (Grandjean et al., 1983). The value of the Eu isomer shift in EuFe4 P12 is −6 mm/s and the isomer shift is independent of temperature from 4 K to 300 K. An isomer shift of −6 mm/s is near the limit for Eu+2 compounds which suggests the possibility of a Eu valence that ﬂuctuates between Eu+2 and Eu+3 conﬁgurations. If the Eu+3 and Eu+2 conﬁgurations are energetically degenerate, the average valence is determined by the degeneracy of each level, which implies a temperature independent valence of about 3 − 8/9 = 2.11. Magnetic order in a mixed valence Eu compound would be extremely interesting. XANES measurements would be helpful in deciding if the Eu valence is intermediate in this material. The reduced moment for Eu+2 , however, may simply indicate an incomplete ﬁlling of the lanthanide site. EuRu4P12 is metallic and orders ferromagnetically for temperatures below 18 K (Grandjean et al., 1983; Sekine et al., 2000b). The saturation moment is about 10% smaller than the Eu+2 value of 7μB which could imply an intermediate Eu valence or an incomplete ﬁlling of the lanthanide site. The value of the Eu isomer shift in EuRu4 P12 is −9.3 mm/s, which is compatible with Eu+2 in a metallic compound. EuFe4Sb12 is metallic and ferromagnetic below 84 K (Dannebrock et al., 1996; E. Bauer et al., 2001a, 2001b). The low temperature saturation moment, however, is only 64% (4.5μB ) of the Eu+2 value of 7μB (Dannebrock et al., 1996; E. Bauer et al., 2001a, 2001b). Part of the decrease is due to the incomplete ﬁlling of the Eu site (E. Bauer et al., 2001a, 2001b) which was estimated to be 84%. The Eu Mössbauer isomer shift is −11.7 mm/s and is temperature independent, which clearly indicates divalent Eu. The remainder of the decrease in the saturation moment was attributed to some type of ferrimagnetism, possibly involving the Fe (E. Bauer et al., 2001a, 2001b). The electrical resistivity is sensitive to the exact ﬁlling of the lanthanide site and the presence of impurity phases. The room temperature resistivity has been reported as low as 38 μ cm (E. Bauer et al., 2001a, 2001b) to 420 μ cm (Kuznetsov and Rowe, 2000). The samples of Kuznetsov and Rowe appear to be of higher quality and phase purity. The room temperature Seebeck coefﬁcient is ≈ 60 μV/K increasing to ≈ 120 μV/K at 800 K (Kuznetsov and Rowe, 2000). The thermoelectric properties of EuFe4 Sb12 are not promising. EuRu4Sb12 is metallic and becomes ferromagnetic for temperatures below 3.3 K (Takeda and Ishikawa, 2000b). The low temperature saturation moment is about 6.2μB , 89% of the Eu+2 value. Low temperature heat capacity measurements indicate that the magnetic entropy removed due to magnetic order is also only about 90% of its expected value (Rln8). It is likely that the lanthanide site is not completely ﬁlled in this compound although mixed valence behavior can not be ruled out with the available data.

11. Gd ﬁlled skutterudites GdFe4 P12 is metallic and a soft ferromagnet with a Curie temperature of 22 K (Jeitschko et al., 2000).

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Fig. 18. Resistivity vs. temperature for a polycrystalline sample of GdRu4 P12 synthesized using high pressures and temperatures (Sekine et al., 2000a).

Fig. 19. Low temperature magnetization curves for GdRu4 P12 that indicate a ﬁeld induced phase transition (Sekine et al., 2000a).

GdRu4 P12 is metallic for temperatures between 30 and 300 K, but undergoes an unusual phase transition near 20 K (ﬁg. 18) (Sekine et al., 2000a). The magnetic susceptibility follows a Curie–Weiss law at high temperatures with effective moment of 8.04μB and a Weiss temperature of +22 K, which suggests ferromagnetic interactions. Below 22 K, however, the magnetization data are more consistent with a strange type of antiferromagnetic ordering. The magnetization data also indicate a ﬁeld-induced phase transition at low temperatures for magnetic ﬁelds ≈ 5–6 T (ﬁg. 19). 12. Tb ﬁlled skutterudites TbRu4 P12 is metallic with unusual phase transitions at 20 K and 10 K (Sekine et al., 2000a). The resistivity data from TbRu4 P12 is similar to that of GdRu4 P12 shown in ﬁg. 18. The high temperature magnetic susceptibility data indicate ferromagnetic interactions (Weiss temperature ≈ 8 K) but low temperature data are more consistent with some type of antiferromagnetic order (ﬁg. 20). Low temperature magnetization data indicate two metamagnetic phase tran-

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Fig. 20. Inverse magnetic susceptibility of TbRu4 P12 vs. temperature measured at H = 1 T. Inset shows an enlarged view of susceptibility data below 20 K (Sekine et al., 2000a).

sitions. It is possible that the unusual phase transitions at about 20 K in both GdRu4 P12 and TbRu4 P12 are related to the freezing of the lanthanide atoms in off-center positions. 13. Yb ﬁlled skutterudites YbFe4 Sb12 was ﬁrst synthesized by Dilley et al. (1998). Measurements of the lattice constant, magnetization, resistivity and heat capacity suggest an intermediate valence for the Yb ions. XANES measurements yield a Yb valence of 2.68 (Leithe-Jasper et al., 1999). The electronic speciﬁc heat coefﬁcient is estimated to be γ = 140 mJ/mol K2 which indicates that the effective mass of the conduction electrons is moderately enhanced at low temperatures. The characteristic temperature, T ∗ , for the Yb valence ﬂuctuations is estimated to be 50 K (see ﬁg. 9a). The Wilson–Sommerfeld ratio, Rw , is about 2.6 in good agreement with the value of Rw = 2 expected for a spin 1/2 Kondo effect. The room temperature value of the resistivity is ≈ 450 μ cm as determined from resistivity and optical measurements (Dordevic et al., 2001) and decreases to ≈ 40 μ cm at 2 K. Optical measurements also are able to directly measure the pseudogap, Δ = 90 cm−1 , created by the hybridization between the Yb 4f states and the extended conduction band states (ﬁg. 21). The mass enhancement scales as m∗ /me = (Δ/T ∗ )2 as predicted by theory (Millis et al., 1987). The thermoelectric properties of YbFe4 Sb12 were investigated by Dilley et al. (1998, 2000a, 2000b), and Kuznetsov and Rowe (2000). The maximum estimated value of ZT is 0.4 at 670 K.

14. Filled skutterudite thermoelectrics 14.1. Introduction to thermoelectric materials and devices As mentioned in sect. 1, in 1996 it was found that some of the lanthanide antimony-based skutterudites had excellent thermoelectric properties above room temperature (Sales et al., 1996;

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Fig. 21. Real part of the conductivity of YbFe4 Sb12 . The symbols on the left axis represent dc values at different temperatures. Below T ∗ (≈ 50 K), a narrow peak at zero frequency and a gap-like feature at ≈ 18 meV gradually develop. Inset: Renormalized band structure calculated from the Anderson lattice Hamiltonian. εk and εf denote bands of free carriers and localized electrons, respectively. At low temperatures a direct gap Δ opens. The Fermi level, EF∗ is near the top of the lower band, Ek− , resulting in hole-like character and enhanced effective mass of the quasiparticles (Dordevic et al., 2001).

Fleurial et al., 1996). This discovery greatly increased the interest in these materials for thermoelectric applications. In addition to the stoichiometric ﬁlled skutterudite compounds of the form RM4 X12 , a large number of related alloys were also investigated as possible thermoelectric materials. Most of the research on lanthanide skutterudites in the context of thermoelectric applications has been reviewed recently by Uher (2001), Nolas et al. (1999), and Sales (1998) and hence only a brief summary of the thermoelectric research will be highlighted in this section. In a solid that conducts both heat and electricity, the thermal and electrical currents are coupled together. This thermoelectric coupling can be used to construct devices that act as refrigerators, power generators or temperature sensors. The devices work because the electrons or holes in a conducting solid also carry heat as well as electrical charge. The electrical carriers are the “working ﬂuid” in a thermoelectric refrigerator. Thermoelectric devices are attractive for many applications as they have no moving parts (except electrons and holes), use no liquid refrigerant and last indeﬁnitely. The major disadvantage of thermoelectric devices is poor efﬁciency. The efﬁciency of a thermoelectric solid is found to depend on material properties through the dimensionless parameter ZT: ZT =

TS2 ρκ

(1)

where T is the absolute temperature, ρ is the electrical resistivity, S is the Seebeck coefﬁcient, and κ is the total thermal conductivity. The total thermal conductivity is often broken up into two parts, κ = κe + κL where κe is the heat carried by the electrons and holes and κL is the heat carried by the lattice. Z is deﬁned as the ﬁgure of merit and ZT is often referred to as the dimensionless ﬁgure of merit. For power generation the efﬁciency is deﬁned as heat in

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Fig. 22. A single thermoelectric couple is illustrated that has been conﬁgured for refrigeration or power generation. The labels “p” (positive) and “n” (negative) refer to the sign of the charge carriers in each leg (open circles correspond to holes and ﬁlled circles to electrons). Refrigeration is possible in these devices because electrons (or holes) carry heat, and hot electrons (holes) can be forced away from the cold end of the device by the battery. If a temperature difference is externally imposed on the device, useful power can be extracted.

divided by work out and is given by: Efﬁciency =

(Th − Tco )(Γ − 1) (Tco + Γ Th )

(2)

where Tco (Th ) is the temperature of the cold (hot) end and Γ = (1 + ZT)1/2 varies with the average temperature T . For refrigeration, efﬁciency is deﬁned as the heat pumped out divided by the work in and is called the Coefﬁcient of Performance (COP). The COP can be greater than 1 and is given by: COP =

(Γ Tco − Th ) . [(Th − Tco )(1 + Γ )]

(3)

For ZT 1, Carnot efﬁciency is obtained for power generation and the Carnot limit to the COP is obtained for refrigeration. Materials currently used in thermoelectric devices have ZT values between 0.4 and 1.0. All thermoelectric devices are composed of thermoelectric couples such as illustrated in ﬁg. 22. Each leg of the couple is a doped semiconductor (or semimetal) with one p-type and one n-type leg. P-type (n-type) means that the dominant charge carriers are positive (negative). One side of the couple is thermally and electrically shorted together using a metal like copper (brown region). Electrical and thermal contact to a heat sink and the battery or load are made through copper pads at the open end of the couple (brown regions). Since the electrons and holes in a material carry heat, a battery can be used to force the hot electrons and holes away from the cold end of the device resulting in cooling of the cold end. If the direction of the current is reversed, the hot and cold ends are also reversed. If a temperature gradient is imposed across the thermoelectric couple, useful power can be extracted. In an actual thermoelectric device, typically several tens of these couples are connected together in series. For good general reviews of thermoelectric devices, materials and theory refer to Rowe (1995), Goldsmid (1986), Mahan et al. (1997), Mahan (1998), Sales (2002), and Nolas et al. (2001). 14.2. Electron crystals and phonon glasses In an ideal thermoelectric material the holes and electrons should have high mobilities and high effective masses. A high mobility and a high effective mass result in a large value of

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Fig. 23. ZT vs. T for several state-of-the-art thermoelectric materials and for a ﬁlled skutterudite with x ≈ 1. (Figure from T.M. Tritt, unpublished.)

Fig. 24. ZT vs. T for two rare-earth-ﬁlled skutterudites. Also shown are the results of a model calculation (squares) (Sales et al., 1997).

S 2 /ρ (see eq. (1) and Goldsmid, 1986). High mobilities are typically found in crystals with a high degree of structural perfection. The ideal thermoelectric material should also have the lowest possible lattice thermal conductivity κL . The lowest possible value of κL for a particular solid is that of a glass with the same chemical composition, κmin (Slack, 1979). The ideal thermoelectric material should therefore conduct electricity like a crystal but conduct heat like a glass. The skutterudite CoSb3 has good electronic properties and can be doped nor p-type (Dudkin and Abrikosov, 1959; Caillat et al., 1996). However, the room temperature lattice thermal conductivity of CoSb3 is ≈ 10 W/m K, which is an order of magnitude too large for a good thermoelectric material. Slack (1995) suggested ﬁlling the voids in the skutterudite structure with weakly bound atoms that “rattle” about their equilibrium positions. He reasoned that heavy “rattlers” with low Einstein temperatures would be effective in scattering the low frequency acoustic phonons that carry most of the heat in a solid. The “rattlers” should therefore dramatically lower κL . What was not clear, however, was how the “rattlers” would alter the electronic conduction. Although the electronic properties of the skutterudite antimonides were somewhat degraded by the presence of various rattlers, there was an overall increase in ZT (Morelli and Meisner, 1995; Sales et al., 1996; Fleurial et al., 1996; Nolas et al., 2000; Tang et al., 2001). Representative thermoelectric data from various ﬁlled skutterudite antimonides are shown in ﬁgs. 23–26. Some of the arsenides and phosphides have been investigated for thermoelectric applications (Watcharapasorn et al., 1999, 2002),

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Fig. 25. ZT vs. T for two Yb ﬁlled skutterudite samples (Nolas et al., 2000).

Fig. 26. ZT vs. T for several ﬁlled skutterudite samples with the composition Cey Fex Co4−x Sb12 (Tang et al., 2001).

but in general these materials are limited by their κL values, which are signiﬁcantly higher than the values for the antimonides. This is not surprising since a lower average mass usually implies a higher sound velocity and a higher κL . 14.3. Future of ﬁlled skutterudites as thermoelectrics The ﬁlled skutterudite antimonides appear to represent excellent examples of electron–crystal, phonon–glass materials. The incoherent rattling of the loosely bound lanthanide atoms in these materials is inferred from the large values of the ADP parameters obtained in single-crystal structure reﬁnements. This rattling lowers the thermal conductivity at room temperature to values within two to three times κmin . The electrical transport in the ﬁlled skutterudites is altered by the presence of the rattlers. Relative to the analogous unﬁlled compounds, the ﬁlled skutterudites exhibit larger effective masses and smaller mobilities. Good overall electrical transport is maintained as indicated by the large values of ZT at elevated temperatures (ﬁgs. 23–26). The high carrier concentrations in the ﬁlled skutterudites are due mostly to the fraction of the lanthanide sites that remain

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empty in samples prepared using equilibrium synthesis methods. A simple semiconductor transport model successfully reproduces most of the qualitative features of the resistivity and Seebeck data from these materials (Sales et al., 1997). By varying the extrinsic carrier concentration in the ﬁlled skutterudites, this model yields a maximum value for ZT of 1.4 at 1000 K, and a maximum ZT value of 0.3 at 300 K. The ZT values of the ﬁlled skutterudites are too small for room temperature applications. The relatively large band gap of these compounds (≈ 0.6 eV) makes it unlikely that further research will result in a skutterudite-based thermoelectric material with properties better than the Bi2 Te3 -based materials currently in use near room temperature (see ﬁg. 23). Only at temperatures in the 600–900 K temperature range are the thermoelectric properties of the ﬁlled skutterudite antimonides of interest for use in power generation applications. Thermoelectric generators using ﬁlled skutterudite antimonides are being investigated by T. Caillat and collaborators at the Jet Propulsion Laboratory. These devices are of interest to NASA as a source of electrical power for deep space missions such as the Cassini and Voyager probes. Filled skutterudites may also be of practical use in the thermoelectric conversion of waste heat into useful electricity. The ﬁlled skutterudite antimonides have demonstrated the validity of the “electron–crystal, phonon–glass” idea in the design of new thermoelectric materials for operation at elevated temperatures. There are many other crystal structures and compounds that contain atomic cages large enough to incorporate additional atoms. It is believed that the ﬁlled skutterudite antimonides only represent a small fraction of a more general class of “rattling semiconductors” and that some of these materials will undoubtedly have high values of ZT at room temperature.

15. Concluding remarks A major theme of contemporary solid state physics is focused on understanding the correlated behavior of electrons in solids. The challenge of this area was succinctly summarized by Anderson’s title “more is different” (1972). The low temperature properties of the lanthanideﬁlled skutterudites touch on many of the exciting topics at the frontier of correlated electron physics. CeFe4 Sb12 and YbFe4 Sb12 are moderately heavy fermion metals. CeRu4 Sb12 exhibits non-Fermi liquid behavior and may be near a ferromagnetic quantum critical point. PrOs4 Sb12 is the ﬁrst example of a Pr compound that exhibits both superconductivity and heavy fermion behavior. PrRu4 P12 and SmRu4 P12 each undergo a metal-to-insulator transition and antiferromagnetic order. PrFe4 P12 is an extremely unusual material in which quadrupolar order (QO) and heavy fermion ground states are extremely close in energy. At low temperatures a magnetic ﬁeld (≈ 4 T) can drive PrFe4 P12 between the two ground states. The density of states in PrFe4 P12 is remarkably sharp in energy as evidenced by a two order of magnitude change in the Hall coefﬁcient below 5 K and a huge value for S at 5 K of −130 μV/K. Most of the La-ﬁlled skutterudites and two of the Pr-ﬁlled skutterudites are superconductors with a maximum Tc of 10.3 K for LaRu4 As12 . Several of the Ce-ﬁlled skutterudites are narrow

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gap semiconductors (also called Kondo insulators) where the gap is created by a strong hybridization between the Ce 4f level and the transition metal and pnicogen states near the Fermi energy. The Nd, Eu, Gd and Tb ﬁlled skutterudites order magnetically at temperatures ranging from 2 K for NdFe4 P12 to 100 K for EuFe4 P12 . The coupling between the lanthanide magnetic moments and the conduction electrons is large in these compounds. This large coupling results in unusual peaks in electrical transport data near the onset of magnetic ordering, and in some cases multiple magnetic transitions. Finally, the thermoelectric ﬁgures of merit for the La, Ce and Yb ﬁlled skutterudites are among the highest values reported for any material at elevated temperatures (600–1000 K). It is hoped that this article has captured some of the excitement generated by the recent research on the lanthanide ﬁlled skutterudites.

Acknowledgements It is a pleasure to thank Peter Khalifah for many constructive comments and suggestions concerning both the science and the presentation of the work summarized in this chapter. Oak Ridge National Laboratory is managed by UT-Battelle, LLC, for the U.S. Department of Energy under Contract No. DE-AC05-00OR22725.

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Caillat, T., Borshchevsky, A., Fleurial, J.-P., 1996. J. Appl. Phys. 80, 4442. Chakoumakos, B.C., Sales, B.C., Mandrus, D., Keppens, V., 1999. Acta Crystall. B 55, 341. Chen, B., Jun-Hao, X., Uher, C., Morelli, D.T., Meisner, G.P., Fleurial, J.-P., Caillat, T., Borshchevsky, A., 1997. Phys. Rev. B 55, 1476. Corbett, J.D., 1985. Chem. Rev. 85, 383. Dannebrock, M.E., Evers, C.B.H., Jeitschko, W., 1996. J. Phys. Chem. Solids 57, 381. Delong, L.E., Meisner, G.P., 1985. Solid State Commun. 53, 119. Dilley, N.R., Freeman, E.J., Bauer, E.D., Maple, M.B., 1998. Phys. Rev. B 58, 6287. Dilley, N.R., Bauer, E.D., Maple, M.B., Sales, B.C., 2000a. J. Appl. Phys. 88, 1948. Dilley, N.R., Bauer, E.D., Maple, M.B., Dordevic, S., Basov, D.N., Freibert, F., Darling, T.W., Migliori, A., Chakoumakos, B.C., Sales, B.C., 2000b. Phys. Rev. B 61, 4608. Dordevic, S.V., Dilley, N.R., Bauer, E.D., Basov, D.N., Maple, M.B., 1999. Phys. Rev. B 60, 11321. Dordevic, S.V., Basov, D.N., Dilley, N.R., Bauer, E.D., Maple, M.B., 2001. Phys. Rev. Lett. 86, 684.

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Shirotani, I., Uchiumi, T., Sekine, C., Hori, M., Kimura, S., Hamaya, N., 1999. J. Solid State Chem. 142, 146. Shirotani, I., Ohno, K., Sekine, C., Yagi, T., Kawakami, T., Nakanishi, T., Takahashi, H., Tang, J., Matsushita, A., Matsumoto, T., 2000. Physica B 281–282, 1021. Singh, D.J., Pickett, W.E., 1994. Phys. Rev. B 50, 11235. Slack, G.A., 1979. In: Solid State Physics, Vol. 34. Academic Press, New York, p. 1. Slack, G.A., 1995. In: CRC Handbook of Thermoelectrics. Chemical Rubber Company, Boca Raton, FL, pp. 407–440. Sofo, J.O., Mahan, G.D., 1998. Phys. Rev. B 58, 15620. Stetson, N.T., Kauzlarich, S.M., Hope, H., 1991. J. Solid State Chem. 91, 140. Sugawara, H., Abe, Y., Aoki, Y., Sato, H., Hedo, M., Settai, R., Onuki, Y., Harima, H., 2000. J. Phys. Soc. Japan 69, 2938. Sugawara, H., Matsuda, T.D., Abe, K., Aoki, K., Sato, H., Nojiri, S., Inada, Y., Settai, R., Onuki, Y., 2001. J. Magn. Magn. Mater. 226, 48. Takeda, N., Ishikawa, M., 2000a. Physica B 281–282, 388. Takeda, N., Ishikawa, M., 2000b. J. Phys. Soc. Japan 69, 868. Takeda, N., Ishikawa, M., 2001. J. Phys. Cond. Mater. 13, 5971. Tang, X., Chen, L., Goto, T., Hirai, T., 2001. J. Mater. Res. 16, 837. Torikachvili, M.S., Chen, J.W., Dalichaouch, Y., Guertin, R.P., McElfresh, M.W., Rossel, C., Maple, M.B., Meisner, G.P., 1987. Phys. Rev. B 36, 8660. Uchiumi, T., Shirotani, I., Sekine, C., Todo, S., Yagi, T., Nakazawa, Y., Kanoda, K., 1999. J. Phys. Chem. Solids 60, 689. Uher, C., 2001. In: Semiconductors and Semimetals, Vol. 69. Academic Press, San Diego, pp. 139–153 (Chapter 5). Watcharapasorn, A., DeMattei, R.C., Feigelson, R.S., Caillat, T., Borshchevsky, A., Snyder, G.J., Fleurial, J.-P., 1999. J. Appl. Phys. 86, 6213. Watcharapasorn, A., Feigelson, R.S., Caillat, T., Borshchevsky, A., Snyder, G.J., Fleurial, J.-P., 2002. J. Appl. Phys. 91, 1344. Wilson, K.G., 1975. Rev. Mod. Phys. 47, 773. Xue, J.S., Antonio, M.A., White, W.T., Soderholm, L., Kauzlarich, S.M., 1994. J. Alloys and Compounds 207–208, 161.

Handbook on the Physics and Chemistry of Rare Earths Vol. 33 edited by K.A. Gschneidner, Jr., J.-C.G. Bünzli and V.K. Pecharsky © 2003 Elsevier Science B.V. All rights reserved

Chapter 212 RARE EARTH –ANTIMONY SYSTEMS Oksana L. SOLOGUB∗ , Petro S. SALAMAKHA Departamento de Quìmica, Instituto Tecnològico e Nuclear, P-2686-953 Sacavèm, Portugal Contents List of symbols and abbreviations 1. Introduction 2. Binary systems 3. Ternary systems 3.1. R–M–Sb systems 3.1.1. Sc–M–Sb systems 3.1.2. Y–M–Sb systems 3.1.3. La–M–Sb systems 3.1.4. Ce–M–Sb systems 3.1.5. Pr–M–Sb systems 3.1.6. Nd–M–Sb systems 3.1.7. Sm–M–Sb systems 3.1.8. Eu–M–Sb systems 3.1.9. Gd–M–Sb systems 3.1.10. Tb–M–Sb 3.1.11. Dy–M–Sb systems 3.1.12. Ho–M–Sb systems 3.1.13. Er–M–Sb systems 3.1.14. Tm–M–Sb systems 3.1.15. Yb–M–Sb systems 3.1.16. Lu–M–Sb systems 3.2. R–R –Sb systems 3.3. R–U–Sb systems 4. Quaternary systems

36 36 36 37 37 37 40 42 49 58 62 72 76 78 82 84 86 88 89 90 92 93 94 95

5. Structure types of the ternary antimonides 6. Physical properties of the ternary antimonides 6.1. RM 2 Sb2 compounds 6.2. RNiSb compounds 6.3. RMSb2 compounds 6.4. R 3 M 3 Sb4 compounds 6.5. R6 MSb15 compounds 6.6. R 14 MSb11 compounds 7. Peculiarities of the interaction of the rare earths and antimony 7.1. Binary systems 7.2. Ternary systems 7.2.1. R–s-element–Sb 7.2.2. R–p-element–Sb 7.2.3. R–d-element–Sb 7.2.4. R–f-element–Sb 7.3. Interconnection of the ternary antimonides with the binary structure types 7.4. Ternary antimonides with the equiatomic composition 7.5. Ternary antimonides with the R:Sb ratio equal to 1:2 Acknowledgement References

95 112 112 115 119 127 133 134 135 135 136 136 136 137 140 140 140 141 142 142

∗ Present address: Institut für Anorganische Chemie, Universität Wien, Währingerstraße 42, A-1090 Wien, Austria.

35

36

O.L. SOLOGUB AND P.S. SALAMAKHA

List of symbols and abbreviations a, b, c at.%

unit cell dimensions (in nm) composition in atomic percent

x, y

indicate variable component contents, when it is used as index in compound compositional

c

concentration

formula. Expressions like: N − x (where N is a

C C

Curie constant speciﬁc heat

number) means N minus x, the x value is given in the text

g

gram

Z

formula per unit cell

h Hcr

hour critical magnetic ﬁeld

∼

is used before the composition formula of a compound to indicate that the composition is

LT HT

low temperature modiﬁcation high temperature modiﬁcation

β

given approximately unit cell angle (in degrees)

M

s-, p-, d- element

χ

magnetic susceptibility

Mx Ny

where x = 2, 3, . . . and y = 0 or 5, M = minimum purity and N = nines

χ0 χC

temperature independent susceptibility diamagnetic susceptibility

R, R

rare earth metal

γ

electronic speciﬁc heat coefﬁcient

S SG

Seebeck coefﬁcient space group

μ θP

magnetic moment paramagnetic Curie temperature

T TC

temperature Curie temperature

θR

characteristic temperature electrical resistivity

0

residual resistivity

TM , Tm temperature of magnetic transition TN

Néel temperature

1. Introduction This chapter presents a review of the current data on phase diagrams and crystal structures of binary, ternary and quaternary metal antimonides with the R elements (R ≡ Sc, Y and the lanthanides). Sections 2–4 give the overview of the literature published on these systems, i.e., the isothermal sections and crystallographic characteristics of the binary, ternary and quaternary compounds, as well as, outlines of the experimental methods that have been utilized. A description of the structure types of ternary antimonides is the subject of sect. 5. The physical properties are only brieﬂy presented for the most common isotypic series of compounds (sect. 6). The general features and trends in the R–Sb and R–(s-, p-, d-, f- element)–Sb systems are discussed in sect. 7. 2. Binary systems Binary systems containing antimony have been investigated by different groups of scientists, and their phase diagrams are mostly compiled by Massalski et al. (1991): Y–Sb (Schmidt and McMasters, 1976), La–Sb (Vogel and Klose, 1954; Lebedev et al., 1983), Ce–Sb (Borsese et al., 1981), Pr–Sb (Abdusalamova et al., 1988), Nd–Sb (Kobzenko et al., 1972), Sm–Sb (Sadygov et al., 1988b; Borzone et al., 1985), Gd–Sb (Abdusalamova et al., 1986), Tb–Sb

RARE EARTH – ANTIMONY SYSTEMS

37

(Abdusalamova et al., 1981), Dy–Sb (Ferro et al., 1988), Ho–Sb (Abdusalamova et al., 1984), Er–Sb (Abdusalamova and Rachmatov, 2000), Tm–Sb (Abdusalamova et al., 1991), Yb–Sb (Bodnar and Steinﬁnk, 1967), Lu–Sb (Abdusalamova et al., 1990). Recently, Borzone et al. (2000) presented modiﬁed phase diagram for the Gd–Sb system. For the other systems only individual alloys were synthesized and investigated with the aim of ﬁnding the isotypic or new compounds. Information on binary compounds is gathered by Villars and Calvert (1985, 1991), and Villars et al. (1995). More recently, the compound Eu16 Sb11 has been prepared from the elements in Ta container by heating at 1370 K and then slowly cooled to 1270 K over 4 days (Chan et al., 2000). This compound is isotypic with the Zintl-phase Ca16 Sb11 (X-ray single crystal diffraction). The crystal structure of the compound previously called “GdSb2 ” was determined by Xray diffraction methods and the true composition was found to be Gd16 Sb39 (Borzone et al., 2000). The high temperature modiﬁcation for the Y5 Sb3 has been reported recently (Mozharivskyj and Franzen, 2000b). Additionally, several compounds not presented on the phase diagrams of the corresponding systems, are listed below. From metallographic analysis of the sample with composition Ce33.3 Sb66.6, Abulkhaev and Abdusalamova (1989) observed, in addition to the expected CeSb2 phase and CeSb, needle shaped single crystals of unknown composition and structure. Authors believe that this phase is a high temperature modiﬁcation of CeSb2 . Altmeyer and Jeitschko (1988) reported the existence of new compound with a monoclinic structure, Dy2 Sb5 , a = 1.3066, b = 0.41627, c = 1.4584, β = 102.21◦. The structure was established by X-ray single crystal diffraction. The Sm2 Sb5 , Gd2 Sb5 and Tb2Sb5 compounds have been found to be isotypic with Dy2 Sb5 (Altmeyer and Jeitschko, 1988). Altmeyer and Jeitschko (1989) observed in the Nd–Sb system at 870 K a new compound with monoclinic symmetry, Nd8+x Sb19+y , a = 2.8495, b = 0.42489, c = 1.34982, β = 95.476◦ (X-ray single crystal investigation). Crystallographic data of the binary antimonides of rare earth are listed in table 1.

3. Ternary systems 3.1. R–M–Sb systems 3.1.1. Sc–M–Sb systems 3.1.1.1. Sc–Co–Sb. The crystal structure of the ScCoSb compound was investigated by Kleinke (1998) by X-ray single crystal diffraction. It was found to crystallize with the TiNiSi structure type (a = 0.6829, b = 0.42401, c = 0.7358). 3.1.1.2. Sc–Ni–Sb. Early investigations of the ScNiSb compound showed that it had the MgAgAs-type with a = 0.6062 (Dwight, 1974) from an X-ray powder analysis of an alloy

38

O.L. SOLOGUB AND P.S. SALAMAKHA Table 1 Crystallographic characteristics of the binary antimonides

Compound

Space group

ScSb Sc5 Sb3 Sc2 Sb YSb2 YSb Y4 Sb3 Y5 Sb3 (LT) Y5 Sb3 (HT) Y3 Sb LaSb2 LaSb LaSb (HP) La4 Sb3 La5 Sb3 La3 Sb2 La2 Sb CeSb2 (HT) CeSb2 CeSb CeSb(HP) Ce4 Sb3 Ce5 Sb3 Ce2 Sb PrSb2 PrSb Pr4 Sb3 Pr5 Sb3 Pr2 Sb Nd8+x Sb19+y

Structure type NaCl Yb5 Sb3 Cu2 Sb HoSb2 NaCl anti-Th3 P4 Mn5 Si3 Yb5 Sb3 Ti3 P SmSb2 NaCl HgMn anti-Th3 P4 Mn5 Si3 unknown own unknown SmSb2 NaCl HgMn anti-Th3 P4 Mn5 Si3 La2 Sb SmSb2 NaCl anti-Th3 P4 Mn5 Si3 La2 Sb own

NdSb2 NdSb Nd4 Sb3 Nd5 Sb3 Nd2 Sb Sm2 Sb5 SmSb2 SmSb Sm4 Sb3 Sm5 Sb3 Sm2 Sb EuSb2 Eu2 Sb3

Fm3m Pnma P4/nmm C222 Fm3m I43d P63 /mcm Pnma P42 /n Cmca Fm3m P4/mmm I43d P63 /mcm

a 0.58517 1.10792 0.42049 0.3283 0.6165 0.905 0.89114 1.1867 1.2361 0.6314 0.6490 0.4019 0.9649 0.942

I4/mmm

0.4626

Cmca Fm3m P4/mmm I43d P63 /mcm I4/mmm Cmca Fm3m I43d P63 /mcm I4/mmm C2/m

0.628 0.6429 0.3975 0.9511 0.931 0.4532 0.626 0.6361 0.948 0.928 0.455 2.8495

SmSb2 NaCl anti-Th3 P4 Mn5 Si3 La2 Sb Dy2 Sb5 own NaCl anti-Th3 P4 Mn5 Si3 La2 Sb CaSb2

Cmca Fm3m I43d P63 /mcm I4/mmm C2/m Cmca Fm3m I43d P63 /mcm I4/mmm P21 /m

0.6230 0.6321 0.9370 0.9170 0.4510 0.6171 0.6268 0.9308 0.8990 0.4468 0.4768

Sr2 Sb3

P21 /c

0.6570

Lattice parameters, nm b 0.87126 0.5907

0.92247 0.6175

c 0.76272 0.77902 0.7981

0.62960 0.80977 0.6180 1.856 0.3279 0.662 1.806

0.613

1.826 0.3244

0.616

0.42489 β = 95.476◦ 0.6063

0.652 1.784 1.816

0.651 1.782 1.34982 1.7892

0.6460 1.7610 0.6051

1.789

0.6138 1.746 0.8970

0.4299 β = 103.01 1.2760 1.5028 β = 90.04 continued on next page

RARE EARTH – ANTIMONY SYSTEMS

39

Table 1, continued Compound

Space group

Eu11 Sb10 Eu16 Sb11 Eu5 Sb3 Gd2 Sb5 Gd16 Sb39

Structure type Ho11 Ge10 Ca16 Sb11 Yb5 Sb3 Dy2 Sb5 own

I4/mmm P-421 m Pnma C2/m C2/m

0.57395

GdSb2 (HT) GdSb2 (LT) GdSb (α) GdSb (β) Gd4 Sb3 Gd5 Sb3 Tb2 Sb5 TbSb2 (HT) TbSb2 (LT) TbSb(α) Tb4 Sb3 (α) Tb5 Sb3 Dy2 Sb5

HoSb2 SmSb2 NaCl unknown anti-Th3 P4 Mn5 Si3 Dy2 Sb5 HoSb2 SmSb2 NaCl anti-Th3 P4 Mn5 Si3 own

C222 Cmca Fm3m

0.3296 0.6157 0.6218

I43d P63 /mcm C2/m C222 Cmca Fm3m I43d P63 /mcm C2/m

0.9220 0.897

DySb2 (HT) DySb(α) Dy4 Sb3 (α) Dy5 Sb3 HoSb2 HoSb Ho4 Sb3 Ho5 Sb3 ErSb2 (HT) ErSb Er4 Sb3 Er5 Sb3 TmSb2 TmSb Tm5 Sb3 YbSb2 YbSb Yb11 Sb10 Yb4 Sb3 Yb5 Sb3 Yb5 Sb3 LuSb2 LuSb Lu5 Sb3 Lu3 Sb

HoSb2 NaCl anti-Th3 P4 Mn5 Si3 own NaCl anti-Th3 P4 Mn5 Si3 HoSb2 NaCl anti-Th3 P4 Yb5 Sb3 HoSb2 NaCl Mn5 Si3 ZrSi2 NaCl Ho11 Ge10 anti-Th3 P4 Mn5 Si3 own HoSb2 NaCl Mn5 Si3 unknown

C222 Fm3m I43d P63 /mcm C222 Fm3m I43d P63 /mcm C222 Fm3m I43d Pnma C222 Fm3m P63 /mcm Cmcm Fm3m I4/mmm I43d P63 /mcm Pnma C222 Fm3m P63 /mcm

a 1.2325 1.2674 1.29826

0.3282 0.6123 0.6178 0.917 0.89324 1.3066 0.3273 0.6154 0.9129 0.8892 0.3343 0.6130 0.9071 0.8851 0.3259 0.6106 0.902 1.1662 0.3252 0.6087 0.4536 0.6082 1.186 0.9320 0.8995 1.2398 0.3244 0.6056 0.890

Lattice parameters, nm b

1.00033 0.4151 β = 99.21 0.5930 0.5986

c 1.8024 1.1720 0.86325 1.3209 0.8030 1.783

0.632 0.5903 0.5969

0.41627 β = 102.21◦ 0.5888

0.7990 1.772

0.62887 1.4584 0.7965

0.5790

0.6270 0.7840

0.5866

0.6234 0.7926

0.9136 0.5851

0.8007 0.7912

1.663

0.4271 1.710

0.9562 0.5935

0.6870 0.8246 0.7885 0.633

40

O.L. SOLOGUB AND P.S. SALAMAKHA

arc melted under argon, annealed at 973 K and furnace cooled. Pecharsky et al. (1983a) conﬁrmed the crystal structure from X-ray powder diffraction and obtained the lattice parameter as a = 0.6055. The stoichiometric amounts of the starting components (Sc 99.5%, Ni (4N), Sb (4N) were arc melted under argon and annealed at 870 K for 200 h. 3.1.1.3. Sc–Pt–Sb. ScPtSb belongs to the MgAgAs-type, a = 0.6312 (Dwight, 1974) (X-ray powder analysis). Sample preparation, see ScNiSb. 3.1.2. Y–M–Sb systems 3.1.2.1. Y–Li–Sb. LaLi3 Sb2 structure type was reported for the YLi3 Sb2 compound, a = 0.45251, c = 0.7158 from X-ray single crystal diffraction (Grund et al., 1984). 3.1.2.2. Y–Zr–Sb. Morozkin and Sviridov (2001) investigated the crystal structure of the YZrSb compound using X-ray powder diffraction (CeScSi structure type, a = 0.4245, c = 1.6306). 3.1.2.3. Y–Ni–Sb. Figure 1 represents the isothermal section of Y–Ni–Sb phase diagram at 870 K (0–50 at.% Sb) which was studied by Zavalii (1982). The isothermal section was constructed by means of X-ray powder analysis of alloys, which were arc melted and subsequently annealed in evacuated silica tubes for 400 h and ﬁnally quenched in water. Starting materials were Y 99.8 wt.%, Ni 99.99 wt.% and Sb 99.99 wt.%. The ternary phase equilibria diagram is characterized by the existence of two ternary compounds: ∼YNi2 Sb2 (1) and ∼YNiSb (2).

Fig. 1. Y–Ni–Sb, partial isothermal section at 870 K (0–50 at.% Sb).

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YNiSb belongs to the MgAgAs-type, a = 0.6312 (Dwight, 1974) from X-ray powder analysis. For sample preparation, see ScNiSb. Sologub et al. (1994) investigated by X-ray powder diffraction the alloy with the nominal composition Y25 Ni25 Sb50 prepared by arc melting ingots of the elements in argon and annealed at 870 K in evacuated quartz tubes for 2 weeks and quenched in water. The sample was found to consist of two phases, namely NiSb (NiAs type, a = 0.3926, c = 0.5134) and YSb (NaCl type, a = 0.61707). The materials used were Y 99.9 wt.%, Ni 99.9 wt.% and Sb 99.9 wt.%. One more ternary compound has been observed and studied by Mozharivskyj and Kuz’ma (1996) from the arc melted, annealed at 1070 K for 400 h, and ﬁnally quenched in cold water alloys. It crystallizes with the Mo5 B2 Si type structure, a = 0.7662, c = 1.3502 (X-ray powder diffraction). The starting metals were Y, not less than 99.8 wt.%, Ni and Sb 99.9 wt.%. Mozharivskyj and Franzen (2000a) studied the crystal structure of Y5 Nix Sb3−x (0 x 0.38) by the X-ray single crystal and powder diffraction. The Yb5 Sb3 structure type (a = 1.1963, b = 0.91330, c = 0.80500) has been observed in the temperature range 1535–1670 K. After annealing the sample for 10 days at 1070 K the structure changes to a Mn5 Si3 structure type. 3.1.2.4. Y–Cu–Sb. No phase diagrams exist for the Y–Cu–Sb system, however two ternary compounds have been observed and characterized. YCuSb2 was found to crystallize with the HfCuSi2 type with the lattice parameters a = 0.42617, c = 0.9903 (Sologub et al., 1994). An alloy with the nominal composition Y25 Cu25 Sb50 was prepared by arc melting ingots of the elements in argon and annealed at 1070 K in evacuated quartz tubes for 2 weeks and quenched in water. The materials used were Y 99.9%, Cu 99.9% and Sb 99.9%. A ternary compound of yttrium with copper and antimony of the stoichiometric ratio 3:3:4 was identiﬁed and studied by means of X-ray analysis by Skolozdra et al. (1993). Y3 Cu3 Sb4 compound was found to have the Y3 Au3 Sb4 type with the lattice parameter of a = 0.9500 (X-ray powder diffraction). The sample was prepared by melting the metals (around 99.8 wt.% pure for yttrium and 99.99 wt.% for copper and antimony) in an arc furnace and annealing at 870 K for 500 h. 3.1.2.5. Y–Pd–Sb. Marazza et al. (1980) established that the YPdSb compound has the MgAgAs type structure with a = 0.6257 using X-ray powder diffraction and metallographic analyses. The sample which was enclosed in tantalum vessel under an argon atmosphere, was prepared by melting in an induction furnace and was then annealed at 780 K for 1 week. The metals used had purities greater than 99.9% for Y and greater than 99.99% for Pd and Sb. YPd2 Sb was reported to be isotypic with the crystal structure of MnCu2 Al with a lattice parameter a = 0.6691 (Ishikawa et al., 1982; powder diffraction). The sample was prepared by levitation melting followed by annealing at 1173 K for several days. Riani et al. (1995) conﬁrmed the crystallographic characteristics for this compound, MnCu2 Al type, a = 0.6691.

42

O.L. SOLOGUB AND P.S. SALAMAKHA

The Y5 Pd2 Sb crystallizes with the Mo5 B2 Si structure type, a = 0.7733, c = 1.3582 (X-ray powder diffraction; Mozharivskyj and Franzen (2000b). The sample was annealed at 1070 K for 10 days. 3.1.2.6. Y–Ag–Sb. YAgSb2 compound was observed and studied by Sologub et al. (1995a). It was found to crystallize with HfCuSi2 -type structure with lattice parameters a = 0.42745, c = 1.0492 (X-ray powder diffraction of arc melted and annealed at 1070 K for 14 days alloy). The purity of starting materials was 99.9 wt.%. The existence and crystal structure of YAgSb2 compound were independently conﬁrmed by Brylak et al. (1995) (a = 0.42765, c = 1.0488; X-ray powder diffraction). The sample was prepared by heating of the mixture of powders of metals with starting composition 1:1:2 in sealed evacuated silica tube for 3 days at 770 K. The reaction product was ground to powder, cold-pressed, sealed again in silica tube, melted in a high frequency furnace, and annealed for 1–2 week at 1070–1170 K. Starting materials were Y 99.9%, Ag M3N, and Sb 325 mesh, M2N5. 3.1.2.7. Y–Te–Sb. Complete c–T diagram was presented for the Sb2 Te3 –Y2 Te3 section by Geidarova and Rustamov (1985). The YTe3 Sb compound formed by incongruent melting was observed and it had the Bi2 Te3 structure type, a = 0.447, c = 3.032 (Geidarova and Rustamov, 1985). 3.1.2.8. Y–Pt–Sb. YPtSb crystallizes with the MgAgAs-type, a = 0.6538 (Dwight, 1974) (X-ray powder analysis). For sample preparation, see ScNiSb. Mozharivskyj and Franzen (2001) reported the crystal structure for the Y5 Pt2 Sb compound from X-ray powder diffraction and it had the Mo5 B2 Si structure, an ordered version of Cr5 B3 structure type, a = 0.7675, c = 1.3575. The starting materials were ingots of Y elements (with purity not less than 99.8%), antimony (99.99%, Johnson Matthey GmbH), and platinum (99.9%, Materials Preparation Center, Ames Laboratory). The mixtures of the components with the initial compositions Y5 Pt2 Sb and with a total weight of 0.5 g were arc-melted in an argon atmosphere, then turned over and remelted to reach homogeneity. The samples were sealed in evacuated silica tubes and annealed at 800 ◦ C for 10 days and then furnace cooled. 3.1.2.9. Y–Au–Sb. A new structure type was reported by Dwight (1977) for the Y3 Au3 Sb4 alloy with a = 0.9818 from X-ray powder diffraction. The conditions of synthesis were not speciﬁed. 3.1.3. La–M–Sb systems 3.1.3.1. La–Li–Sb. A unique structure type was observed for the LaLi3 Sb2 compound, a = 0.4619, c = 0.7445 from X-ray single crystal diffraction (Grund et al., 1984). 3.1.3.2. La–Mg–Sb. No phase diagram exists for the La–Mg–Sb system. The formation of three compounds was reported by Ganguli et al. (1993) from X-ray single crystal investigations: La4 Mg4.48Sb7 , own structure type, a = 0.46201, c = 2.6069; La4.89Mg1.539Sb6 ,

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43

own structure type, a = 0.4616, c = 6.767; La3 Mg4.6 Sb6 , own structure type, a = 0.4625, c = 6.691. 3.1.3.3. La–Al–Sb. Muravjova (1971) has investigated the La–Al–Sb ternary system (0– 33 at.% of La) at 773 K. No ternary phases have been found. 3.1.3.4. La–Ti–Sb. The crystal structure of the La3 TiSb5 compound was investigated by Bollore et al. (1995). The Hf5 CuSn5 anti-type was established (a = 0.9528, c = 0.6278, X-ray single crystal diffraction). 3.1.3.5. La–V–Sb. The only information available on the interaction of the components in the La–V–Sb system is the formation of the LaVSb3 compound observed by Brylak and Jeitschko (1995). It was reported to adopt the CeCrSb3 type structure, a = 1.3358, b = 0.62583, c = 0.60551 from X-ray powder diffraction. 3.1.3.6. La–Cr–Sb. LaCrSb3 crystallizes with a CeCrSb3 type, a = 1.3276, b = 0.6209, c = 0.6114 (X-ray powder diffraction; Brylak and Jeitschko, 1995). Ferguson et al. (1997) and Raju et al. (1998) conﬁrmed the crystal structure using single crystal (a = 1.32835, b = 0.62127, c = 0.6116) and powder diffraction (a = 1.3264, b = 0.6182, c = 0.6094) respectively. 3.1.3.7. La–Mn–Sb. Cordier et al. (1985) reported on the crystal structure for the LaMn0.65−0.76 Sb2 compound (HfCuSi2 -type, a = 0.4387–0.4372, c = 1.0780–1.0933; X-ray single crystal method). Sologub et al. (1995b) observed the ternary phase isotypic with HfCuSi2 from the alloy with slight different metal deﬁciency, LaMn0.87Sb2 (a = 0.43657, c = 1.0924; X-ray powder diffraction). Sample was prepared by arc melting ingots of the elements in argon under a low electric current. The weight losses were compensated by adding beforehand an extra amount of Mn. The resulting button was annealed at 1070 K for 350 h. The purity of starting materials was 99.9 wt.%. Wollesen et al. (1996) conﬁrmed the crystal structure using a single crystal method: a = 0.4381, c = 1.0772 for LaMn0.721(1)Sb2 . The sample was prepared by annealing cold-pressed pellets of the elemental components taken with the atomic ratio of 1:1:2 in evacuated sealed silica tubes for 10 days at 1070 K followed by cooling at a rate of 100 ◦ C/h. Purities of starting elements were La, greater than 99.9%, Mn, greater than 99.8%, Sb 99.9%. The crystal structure of the La6 MnSb15 compound was investigated by Sologub et al. (1996b) by X-ray single crystal and powder diffraction. It was found to crystallize with its own structure type, a = 1.5376, b = 1.9611, c = 0.4314. The single crystal was grown from a melt of the nominal composition LaMn0.25Sb2 . The sample with a total mass 5 g was heated in a corundum crucible in an argon atmosphere to 1500 K and cooled to room temperature with at a rate of 100 K/h. 3.1.3.8. La–Fe–Sb. Leithe-Jasper and Rogl (1994) investigated the formation and crystal structure of the LaFe1−x Sb2 compound by X-ray powder analysis of the alloys

44

O.L. SOLOGUB AND P.S. SALAMAKHA

La30−31Fe13−14 Sb57−55 (HfCuSi2 -type, a = 0.44028–0.44035, c = 1.00119–1.00113). The alloys were obtained by arc melting under low electric current to minimize weight losses by vaporization of Sb, which were compensated beforehand by extra amounts of Sb. The samples were placed in alumina crucibles, sealed in evacuated quartz tubes and annealed for 7 days at 1070 K. After the heat treatment the alloys were quenched by submerging the silica tubes in water. The materials used were 99.9% pure. The crystal structure of the LaFe4 Sb12 compound was investigated by Braun and Jeitschko (1980). It was found to adopt the LaFe4 P12 type structure, a = 0.91395 (X-ray single crystal method). The purities of the materials were 99.9% or better. Filings of the lanthanum were prepared under argon and annealed with the corresponding amounts of antimony in evacuated sealed silica tubes for two days at 723 K, followed by ﬁve days at 1023 K. The resulting antimonide LaSb was ground together with appropriate amounts of Fe and Sb, pressed into pellets and sealed in evacuated silica tubes. The ampules were quickly heated to 1150 K, were kept at this temperature for 3 h and were then quenched. The starting composition was La:Fe:Sb = 1:4:20. The excess antimony was removed by treating the product for several minutes with concentrated nitric acid. The oxidation products of antimony were then dissolved in concentrated hydrochloric acid. 3.1.3.9. La–Co–Sb. Cordier et al. (1985) reported on the crystal structure for the LaCo0.68Sb2 compound (HfCuSi2 -type, a = 0.4394, c = 0.9954; X-ray single crystal method). LeitheJasper and Rogl (1994) investigated the formation and crystal structure of the LaCo1−x Sb2 compound by X-ray powder analysis of the alloy La30 Co15 Sb55 (HfCuSi2 -type, a = 0.43854, c = 0.99232). For sample preparation and purity of starting materials, see LaFe1−x Sb2 . Wollesen et al. (1996) conﬁrmed the crystal structure by using X-ray powder diffraction: a = 0.43843, c = 0.99286 for LaCo1−x Sb2 . For synthesis, see LaMn0.721(1)Sb2 . Purities of starting elements were La, greater than 99.9%, Co, greater than 99.8%, Sb 99.9%. From a room temperature X-ray powder diffraction analysis La6 Co13 Sb was found to crystallize with the ordered La6 Co11 Ga3 , i.e., the Nd6 Fe13 Si type structure, a = 0.8097, c = 2.3289 (Weitzer et al., 1993). An alloy was synthesized from ingots and compacted powders of the constituting elements (99.9% pure) by arc-melting, followed by annealing at 1073 for 5 days and quenched in cold water. 3.1.3.10. La–Ni–Sb. The isothermal section of the La–Ni–Sb phase diagram at 870 K studied by Zavalii (1982) is shown in ﬁg. 2. The isothermal section was constructed by means of X-ray powder analysis of alloys, which were arc melted and subsequently annealed in evacuated silica tubes for 400 h and ﬁnally quenched in water. Starting materials were La 99.8 wt.%, Ni 99.99 wt.% and Sb 99.99 wt.%. The ternary phase equilibria diagram is characterized by the existence of three ternary compounds: LaNi2±x Sb2±x (1), LaNiSb2±x (2) and LaNiSb (3). LaNiSb was found to crystallize with the ZrBeSi type with lattice parameters of a = 0.4404, c = 0.8403 (Hartjes and Jeitschko, 1995; X-ray powder diffraction). Cold-pressed pellets of the ideal composition were arc melted in an atmosphere of argon and annealed at 1120 K for one week. Purities of starting materials were better than 99.9%.

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45

Fig. 2. La–Ni–Sb, isothermal section at 870 K.

Structure reﬁnement from single crystal data established the CaBe2 Ge2 type structure for the compound LaNi1.51Sb2 : a = 0.4466, c = 0.991 (Hoffman and Jeitschko, 1988). The single crystal was selected from a sample prepared by annealing the elemental components for 5 days at 1073 K. The resulting button was melted in a high-frequency furnace and quenched. The CaBe2 Ge2 type was conﬁrmed from an arc melted alloy of the LaNi2 Sb2 composition; a monoclinic distortion was observed after annealing it at 1070 K for one week (X-ray powder diffraction; Slebarski et al., 1996). Pecharsky et al. (1981) reported the BaAl4 type structure with a = 0.4433, c = 1.0024 for the LaNi2 Sb2 compound obtained by arc-melting and annealing at 670 K. LaNiSb2 was found to adopt the HfCuSi2 type structure with the lattice parameters of a = 0.44269, c = 0.9876 (Sologub et al., 1994). The alloy was prepared by arc melting ingots of the elements with the nominal composition La25 Ni25 Sb50 in argon and annealed at 870 K in evacuated quartz tubes for 2 weeks and quenched in water. The materials used were La 99.9%, Ni 99.9% and Sb 99.9%. Hoffman and Jeitschko (1988) investigated the antimony rich section of the ternary system La–Ni–Sb from the samples quenched from 1070 K. Except for LaNi2−x Sb2 , no other ternary compound with a high antimony content was observed. In the various samples, LaNi2−x Sb2 was found to be in equilibrium with LaSb, LaSb2 , NiSb and the high temperature modiﬁcation of Ni3 Sb. 3.1.3.11. La–Cu–Sb system. The isothermal section of the La–Cu–Sb system at 870 K was constructed by Protsyk et al. (2000) (ﬁg. 3). The alloys were synthesized by arc-melting the starting components in an argon atmosphere. The resulting buttons were annealed at 870 K

46

O.L. SOLOGUB AND P.S. SALAMAKHA

Fig. 3. La–Cu–Sb, isothermal section at 870 K.

for two weeks. Four ternary compounds were observed: ∼LaCu6 Sb3 (1), LaCu1−x Sb2 (2), La3 Cu3 Sb4 (3) and La6 CuSb15 (4). A ternary compound of lanthanum with copper and antimony of the stoichiometric ratio 3:3:4 was identiﬁed and studied by means of X-ray analysis by Skolozdra et al. (1993). La3 Cu3 Sb4 (3) compound was found to have the Y3 Au3 Sb4 type with the lattice parameter of a = 0.9837 (X-ray powder diffraction). For experimental details, see the Y–Cu–Sb system. A HfCuSi2 -type structure was reported for the LaCu0.82−0.87 Sb2 compound (2), a = 0.4402–0.4373, c = 1.0154–1.0400 (X-ray single crystal method; Cordier et al. (1985). The crystallographic characteristics for LaCuSb2 were conﬁrmed by Sologub et al. (1994) from X-ray powder diffraction: HfCuSi2 type, a = 0.43690, c = 1.0376. For experimental details, see LaNiSb2 . The crystal structure of the La6 CuSb15 (4) compound was investigated by Sologub et al. (1996b) by X-ray single crystal and powder diffraction. It was found to crystallize with a La6 MnSb15 structure type, a = 1.5395, b = 1.9465, c = 0.4333. For the sample preparation, see La6 MnSb15. The crystal structure of ∼LaCu6 Sb3 (1) compound is unknown. 3.1.3.12. La–Zn–Sb system. Cordier et al. (1985) reported on the crystal structure for the LaZn0.52Sb2 compound (HfCuSi2 -type, a = 0.4380, c = 1.0488; X-ray single crystal method). Wollesen et al. (1996) conﬁrmed the crystal structure using X-ray powder diffraction: a = 0.43883, c = 1.0508 for LaZn1−x Sb2 . For experimental details, see

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47

LaMn0.721(1)Sb2 . Purities of starting elements were La, greater than 99.9%, Zn, greater than 99.8%, Sb 99.9%. Salamakha and Mudryi (2001a) studied the crystal structure of the LaZn0.6Sb2 compound. The sample was synthesized in two stages. The proper amounts of the powders were compacted and sealed in evacuated silica capsule. After slowly heating to 1070 K (1st stage), the sample was studied by X-ray powder diffraction. Afterwards, the pellet was reground under C6 H12 , recompacted and annealed at 870 K for 150 h (2nd stage). The purity of starting materials was 99.9 wt.%. Two modiﬁcations of LaZn0.6Sb2 compound were observed: a = 0.43794, b = 0.44022, c = 1.05044, NdAgAs2 type structure (for the sample after 1st stage of annealing) and a = 0.43900, c = 1.0508, HfCuSi2 type structure (for the sample after 2nd stage of annealing). The crystal structure of the La6 ZnSb15 compound was investigated by Sologub et al. (1996b) by an X-ray single crystal and powder diffraction. It was found to crystallize with the La6 MnSb15 structure type, a = 1.5430, b = 1.9461, c = 0.4351. For the sample preparation, see La6 MnSb15. 3.1.3.13. La–Ga–Sb. Mills and Mar (2000) reported on the existence of three ternary compounds: La13Ga8 Sb11 , La12 Ga4 Sb23 and LaGaSb2 . The samples have been synthesized by direct reaction of the elements in evacuated silica tubes. The crystal structure of the La13 Ga8 Sb11 compound was determined by X-ray single crystal diffraction: own structure type, space group P6/mmm, a = 1.7657, c = 0.43378. The compound La12 Ga4 Sb23 was found to adopt the Pr12 Ga4 Sb23 type structure with the lattice parameters of a = 0.4344, b = 1.9750, c = 2.6860 (X-ray powder diffraction). The crystal structure of the LaGaSb2 compound is unknown. 3.1.3.14. La–Ge–Sb. Lam et al. (2001) determined the crystal structure of the La6 Ge2.8Sb13.2 compound (own structure type, a = 0.43034, b = 1.0851, c = 2.7073) by X-ray single crystal diffraction. The sample had been synthesized by direct reaction of the elements at 1223 K. 3.1.3.15. La–Zr–Sb. The crystal structure of the La3 ZrSb5 compound was investigated by Bollore et al. (1995). It was found to adopt the Hf5 CuSn3 anti-type structure, a = 0.9587, c = 0.6258 (X-ray powder diffraction). Ferguson et al. (1997) conﬁrmed the crystal structure of the La3 ZrSb5 compound using single crystal X-ray diffraction (a = 0.95743, c = 0.63495). 3.1.3.16. La–Nb–Sb. Bollore et al. (1995) determined the crystal structure of La3 NbSb5 to have the Hf5 CuSn3 anti-type structure, a = 0.9534, c = 0.6264 (X-ray powder diffraction). 3.1.3.17. La–Ru–Sb. The crystal structure of the LaRu4 Sb12 compound was studied by Braun and Jeitschko (1980). It was found to crystallize with the LaFe4 P12 type, a = 0.92700 (X-ray powder diffraction). The purities of starting materials and experimental procedure were the same as for LaFe4 Sb12.

48

O.L. SOLOGUB AND P.S. SALAMAKHA

3.1.3.18. La–Rh–Ge. Malik and Adroja (1991b) established the KHg2 type structure with a = 0.4646, b = 0.7547, c = 0.7898 for the LaRhSb compound using X-ray powder diffraction of an arc melted alloy. Purities of the metals were better than 99.99%. Accordingly to Zeng and Franzen (2000), the La0.1 Rh8 Sb24 compound belongs to a LaFe4 P12 type, a = 0.92213 (X-ray single crystal diffraction). Menon Latica and Malik (1996) reported the existence of LaRh2 Sb2 with a tetragonal structure, but no lattice constants were reported. 3.1.3.19. La–Pd–Sb. Marazza et al. (1980) established the CaIn2 type structure with a = 0.4610, c = 0.8115 for the LaPdSb compound using X-ray powder diffraction and metallographic analyses. For the sample preparation and purity of starting components, see Y–Pd– Sb system. Malik and Adroja (1991a) conﬁrmed the crystal structure and lattice parameters, a = 0.4596, c = 0.8094 (X-ray diffraction, arc melted alloy). LaPdSb2 was found to form the HfCuSi2 type structure with the lattice parameters of a = 0.45309, c = 0.9989 (Sologub et al., 1994). For experimental details, see LaNiSb2 . Hoffman and Jeitschko (1985) established the CaBe2 Ge2 type structure for LaPd2 Sb2 , a = 0.4627, c = 1.0422, X-ray powder diffraction. Mixtures of the elemental components were cold pressed, melted in a high frequency furnace, annealed for 3 days at 1170 K and oven cooled. 3.1.3.20. La–Ag–Sb. LaAgSb2 compound was observed and studied by Sologub et al. (1995a). It was found to crystallize with HfCuSi2 type structure with lattice parameters of a = 0.43898, c = 1.0842 by X-ray powder diffraction of arc-melted and annealed at 870 K for 14 days alloy. The purity of the starting materials was 99.9 wt.%. The existence and crystal structure of LaAgSb2 compound were independently conﬁrmed by Brylak et al. (1995) (a = 0.43903, c = 1.0840; X-ray powder diffraction). For sample preparation, see YAgSb2 . The starting materials purities were: La 99.9%, Ag M3N, and Sb 325 mesh, M2N5. 3.1.3.21. La–Cd–Sb. Sologub et al. (1995b) reported on the crystallographic data for the LaCdSb2 compound (HfCuSi2 type structure, a = 0.44048, c = 1.0991; X-ray powder diffraction) obtained from a multiphase alloy. For the sample preparation and purity of the starting materials, see CeZn1−x Sb2 . Wollesen et al. (1996) conﬁrmed the crystal structure by using a single crystal method: a = 0.4399, c = 1.0997 for CeCd0.700(1)Sb2 . For experimental details, see LaMn0.721(1)Sb2 . Purities of starting elements were La, greater than 99.9%, Cd, greater than 99.8%, Sb 99.9%. 3.1.3.22. La–In–Sb. The crystal structure of the LaIn0.8Sb2 compound was investigated by Ferguson et al. (1999) using X-ray single crystal and powder diffraction: own structure type, space group P21/m, a = 0.4521, b = 0.4331, c = 1.1914, β = 99.66◦. 3.1.3.23. La–Sn–Sb. La4 SnSb2 was investigated by X-ray powder diffraction; the Th3 P4 type structure was established, a = 0.9686 (Hulliger and Ott, 1977). For synthesis, see La4 PbSb2 .

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Wang et al. (1967) studied the LaSn2 –LaSb2 section and reported the existence of a ternary compound that they tentatively identiﬁed as LaSnSb2 . Ferguson et al. (1996) has determined the crystal structure of LaSnx Sb2 from single crystal X-ray diffraction method: own structure type, space group Cmcm, a = 0.42425, b = 2.3121, c = 0.45053 (for x = 0.75). The homogeneity range has been established for the LaSnx Sb2 (0.1 x 0.8) compound. The samples were synthesized by the direct reaction of the elements at 1223 K. 3.1.3.24. La–Hf–Sb. The crystal structure of the La3 HfSb5 compound was investigated by Bollore et al. (1995). It was found to adopt the Hf5 CuSn3 anti-type structure, a = 0.9582, c = 0.6356 (X-ray powder diffraction). Ferguson et al. (1997) determined the crystal structure of the compound La5 HfSb5 by using a single crystal method: a = 0.9557, c = 0.63388. 3.1.3.25. La–Os–Sb. Braun and Jeitschko (1980) investigated the crystal structure of the LaOs4 Sb12 compound. It was found to form the LaFe4 P12 type structure, a = 0.93029 (X-ray powder diffraction). The purities of starting materials and experimental procedure were the same as for LaFe4 Sb12 . 3.1.3.26. La–Pt–Sb. LaPtSb crystallizes with the CaIn2 -type structure, a = 0.4560, c = 0.8263 (Rossi et al., 1981; powder X-ray diffraction data). The starting elements (La 3N, Pt 4N, Sb 4N) were melted under argon in tantalum crucible, and annealed at 773 K for one week. 3.1.3.27. La–Au–Sb. LaAuSb2 was found to adopt the HfCuSi2 type structure with the lattice parameters as a = 0.44363, c = 1.0434 (Sologub et al., 1994). The alloy was prepared in the same manner as YCuSb2 . Wollesen et al. (1996) conﬁrmed the crystal structure by using a single crystal method: a = 0.4436, c = 1.0432. The single crystal was isolated from the sample where the elemental components were annealed together in a NaCl/KCl (1:1) ﬂux for 1 week at 1070 K. The purities of the starting elements were La, greater than 99.9%, Au, greater than 99.9%, Sb 99.9%. Kasaya et al. (1991) reported an Y3 Au3 Sb4 type structure for the compound La3 Au3 Sb4 , a = 1.0123 (powder diffraction; powder metallurgical technique). 3.1.3.28. La–Pb–Sb. La4 PbSb2 was investigated by X-ray powder diffraction; the Th3 P4 type structure was established, a = 0.9707 (Hulliger and Ott, 1977). The sample was obtained by heating a mixture of the starting components (with purity (3N) in sealed tantalum tube at 50–100◦ below the melting point for 8 h. The formation and crystal structure of the La5 Pb3 Sb compound with the Ti5 Ga4 type structure was observed by Guloy and Corbett (1994) from X-ray powder diffraction of the sample prepared by a powder metallurgical technique. 3.1.4. Ce–M–Sb systems 3.1.4.1. Ce–Li–Sb. No ternary phase diagram exists for the Ce–Li–Sb system; however the formation of one ternary compound has been reported by Fischer and Schuster (1982):

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Fig. 4. Ce–Si–Sb, isothermal section at 670 K.

CeLi2 Sb2 , CaAl2 Si2 type structure, a = 0.4311, c = 0.6984. The alloy was prepared by heating the elements in a Ta crucible at 870–1170 K for 24–48 h. 3.1.4.2. Ce–Si–Sb. The isothermal section of the phase diagram of the Ce–Si–Sb system (ﬁg. 4) was constructed from an X-ray analysis of 55 alloys prepared by arc melting in an argon atmosphere and annealed in quartz ampoules under vacuum at 670 K for 500 h (Stetskiv, 1999). The purity of the starting metals was better than 99.9 at.%. Two ternary compounds ∼Ce2 Si3 Sb5 (1) (unknown structure), and Ce3 SiSb (2) (La3 GeIn type structure, a = 1.1948, c = 1.5484) were found. The binary compounds CeSb2 , CeSb, Ce2 Sb and CeSi2−x dissolve less than 5 at.% of Sb or Si. 3.1.4.3. Ce–Ti–Sb. The crystal structure of the Ce3 TiSb5 compound was investigated by Bollore et al. (1995). It was found to form the Hf5 CuSn3 anti-type structure, a = 0.9439, c = 0.6235 (X-ray powder diffraction). 3.1.4.4. Ce–V–Sb. CeVSb3 crystallizes with the CeCrSb3 type structure, a = 1.3119, b = 0.62392, c = 0.60303 (X-ray powder diffraction; Brylak and Jeitschko, 1995). 3.1.4.5. Ce–Cr–Sb. A unique type of structure was reported for CeCrSb3 , a = 1.3108, b = 0.6184, c = 0.6079 (X-ray single crystal data; Brylak and Jeitschko, 1995). Ferguson et al. (1997) conﬁrmed the structure from X-ray powder diffraction: a = 1.3127, b = 0.6199, c = 0.6092. 3.1.4.6. Ce–Mn–Sb. The phase equilibria were established in the ternary system Ce–Mn– Sb for an isothermal section at 870 K (ﬁg. 5). Three ternary compounds were observed:

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Fig. 5. Ce–Mn–Sb, isothermal section at 870 K.

CeMn0.85Sb2 (1), Ce29 Mn13Sb58 (2) and Ce6 MnSb15 (3) (Sologub et al., 1995c). The samples were generally prepared by arc melting proper amounts of constituent elements and annealing for 250 h at 870 K. Ternary alloys in the region of 30 to 50 at.% Sb were prepared by heating of compacted mixtures of powders in evacuated quartz tubes from 470 to 870 during a 75 h period, then recompacted and heated at 870 K for 150 h, and ﬁnally quenched in cold water. Sologub et al. (1995b) reported on the crystal structure for the CeMn0.85Sb2 compound (HfCuSi2 type structure, a = 0.43439, c = 1.0756; X-ray powder diffraction). For experimental details, see LaMn0.87Sb2 . Wollesen et al. (1996) conﬁrmed the crystal structure by using a single crystal method: a = 0.43514, c = 1.0690 for CeMn0.741(8)Sb2 . For experimental details, see LaAuSb2 . The purities of the starting elements were Ce, greater than 99.9%, Mn, greater than 99.8%, Sb 99.9%. The crystal structure of the Ce6 MnSb15 compound was investigated by Sologub et al. (1996b) by X-ray powder diffraction. It was found to crystallize with the La6 MnSb15 structure type, a = 1.51538, b = 1.93646, c = 0.42742. The sample was prepared by arc melting of ingots of the starting elements (purity 99.9 wt.%). Arc melted buttons were annealed at 870 K for 170 h and ﬁnally quenched by submerging the capsules into cold water. The crystal structure of Ce29 Mn13Sb58 compound was not studied (Sologub et al., 1995c). 3.1.4.7. Ce–Fe–Sb. The formation and crystal structure of the CeFe1−x Sb2 compound were studied by Leithe-Jasper and Rogl (1994) from X-ray powder analysis of the alloy Ce30−28 Fe13−17Sb57−55 (HfCuSi2 type structure, a = 0.43751–0.43768, c = 0.98218– 0.98271). For sample preparation and purity of starting materials, see LaFe1−x Sb2 .

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Fig. 6. Ce–Ni–Sb, isothermal section at 870 K.

The crystal structure of the CeFe4 Sb12 compound was investigated by Braun and Jeitschko (1980). It was found to adopt the LaFe4 P12 type, a = 0.91350 (X-ray powder diffraction). The purities of starting materials and experimental procedure were the same as for LaFe4 Sb12 . Kaiser and Jeitschko (1999) investigated the phase relations in the Ce–Fe–Sb ternary system at 1173 K for the antimony-rich corner. They found three ternary compounds: CeFeSb2 , CeFe4 Sb12 and Ce2 Fe4 Sb5 . 3.1.4.8. Ce–Co–Sb. Leithe-Jasper and Rogl (1994) investigated the formation and crystal structure of the CeCo1−x Sb2 compound from X-ray powder analysis of the alloy Ce30−25 Co15−25Sb55−50 (HfCuSi2 type structure, a = 0.43588–0.43747, c = 0.97479– 0.98214). For sample preparation and purity of starting materials, see LaFe1−x Sb2 . Wollesen et al. (1996) conﬁrmed the crystal structure by using X-ray powder diffraction: a = 0.43579, c = 0.9771 for CeCo1−x Sb2 . For synthesis, see LaMn0.721(1)Sb2 . The purities of starting elements were Ce, greater than 99.9%, Co, greater than 99.8%, Sb 99.9%. 3.1.4.9. Ce–Ni–Sb. The isothermal section of Ce–Ni–Sb phase diagram at 870 K studied by Pecharsky et al. (1983b) is given in ﬁg. 6. For the sample preparation, see the La–Ni–Sb system. The ternary phase equilibria diagram is characterized by the existence of three ternary compounds: CeNiSb2±x (1), CeNi2±x Sb2±x (2) and CeNiSb (3). Pankevich et al. (1983) reported the crystal structure for the CeNiSb2 compound, HfCuSi2 type structure, a = 0.4409, c = 0.9750 (X-ray powder diffraction; arc melted and annealed at 870 K for two weeks). The crystallographic characteristics were conﬁrmed by Sologub et al. (1994), a = 0.43934, c = 0.9750 and Skolozdra et al. (1994). For experimental details, see LaNiSb2 . Early investigations of the CeNiSb compound showed that it had the AlB2 -type with a = 0.4384, c = 0.4110 (Pecharsky et al., 1983a; X-ray powder analysis). For experimental

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Fig. 7. Ce–Cu–Sb, isothermal section at 870 K.

procedure, see ScNiSb. At variance with these data, Hartjes and Jeitschko (1995) suggested the ZrBeSi type structure, a = 0.4393, c = 0.8257 from X-ray powder diffraction. For experimental details, see LaNiSb. The CeGa2 Al2 type structure was proposed for the CeNi2 Sb2 compound by Pecharsky et al. (1983b), a = 0.4395, c = 0.9981 from X-ray powder diffraction of an alloy which was arc melted under argon, annealed at 870 K and quenched. The starting components were Ce 99.5%, Ni and Sb (4N). Hoffman and Jeitschko (1988) established a defect CaBe2 Ge2 structure for CeNi2−x Sb2 alloy, a = 0.4413, c = 0.9846, X-ray powder diffraction. Mixtures of the elemental components were annealed for about one week between 1023 K and 1073 K, ground to powder, cold pressed, melted in a high frequence furnace and quenched. A unique structure type was reported for the compound CeNi2+x Sb2−x a = 0.4312, b = 0.4285, c = 1.0205 (Pecharsky et al., 1982; X-ray powder diffraction). 3.1.4.10. Ce–Cu–Sb. Isothermal section at 870 K for the Ce–Cu–Sb system was constructed by Protsyk et al. (2000) (ﬁg. 7). For experimental procedures, see La–Cu–Sb. Four ternary compounds were observed: ∼CeCu6 Sb3 (1), CeCu1−x Sb2 (2), Ce3 Cu3 Sb4 (3) and Ce6 CuSb15 (4). CeCuSb2 was found to form a HfCuSi2 type with the lattice parameters of a = 0.43378, c = 1.02333 (Sologub et al., 1994). For experimental details, see LaNiSb2 . A ternary compound of cerium with copper and antimony of the stoichiometric ratio 3:3:4 was identiﬁed and studied by means of X-ray analysis by Skolozdra et al. (1993). Ce3 Cu3 Sb4 compound was found to have the Y3 Au3 Sb4 type with the lattice parameters of a = 0.9721 (X-ray powder diffraction). For experimental details, see the Y–Cu–Sb system. At variance with this data, Patil et al. (1996) reported a tetragonal distortion of the cubic crystal structure Y3 Cu3 Sb4 for the Ce3 Cu3 Sb4 alloy which was prepared by arc melting the constituent ele-

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ments of purity better than 99.9% in an argon atmosphere and annealed at 1070 K for one week (a = 0.971, c = 0.998; X-ray powder diffraction). The crystal structure of the Ce6 CuSb15 compound was investigated by Sologub et al. (1996b) by the X-ray powder diffraction. It was found to crystallize with a La6 MnSb15 structure type, a = 1.5452, b = 1.9178, c = 0.4378. The sample was synthesized in the same manner as Ce6 MnSb15. CeCu1.33 Sb2 was found to crystallize with the CaBe2 Ge2 type structure a = 0.4341, c = 1.0256 from X-ray powder diffraction (Mentink et al., 1994). The starting materials Ce, Cu, Sb were 3 nines pure. The sample was arc melted, wrapped in Ta foil and annealed at 1073 K for 4 weeks. Guzik et al. (1996) reported the crystal structure investigation for the compound with a nominal composition CeCu1.8 Sb2 : CaBe2 Ge2 type structure, a = 0.437, c = 1.023 (X-ray powder diffraction, arc melted and annealed at 970 K for one week sample). 3.1.4.11. Ce–Zn–Sb. Sologub et al. (1995b) reported on the crystal structure for the CeZn1−x Sb2 compound (HfCuSi2 type structure, a = 0.43605, c = 1.0409; X-ray powder diffraction). The sample was obtained via a powder metallurgical reaction. The thoroughly mixed blends of powders were compacted and sealed in evacuated silica capsules. After slowly heating to about 870 K for a ﬁrst reaction, the pellets were reground under C6 H12 and recompacted for ﬁnal heat treatment at 870 K for 350 h. The purity of starting materials was 99.9 wt.%. Wollesen et al. (1996) conﬁrmed the crystal structure using X-ray powder diffraction: a = 0.43449, c = 1.05834 for CeZn1−x Sb2 . For experimental details, see LaMn0.721(1)Sb2 . Purities of starting elements were Ce, greater than 99.9%, Zn, greater than 99.8%, Sb 99.9%. Salamakha and Mudryi (2001a) studied the crystal structure of the CeZn0.8Sb2 compound. The sample was synthesized in two stages. Proper amounts of powder were compacted and sealed in evacuated silica capsule. After slowly heating to 1070 K (1st stage), the sample was studied by X-ray powder diffraction. Afterwards, the pellet was reground under C6 H12 , recompacted and annealed at 870 K for 150 h (2nd stage). The purity of starting materials was 99.9 wt.%. Two modiﬁcations of CeZn0.8 Sb2 compound were observed to form: a = 0.43493, b = 0.43742, c = 1.04763, NdAgAs2 type structure (for the sample after 1st stage of annealing) and a = 0.43635, c = 1.04160, HfCuSi2 (for the sample after 2nd stage of annealing). The crystal structure of the Ce6 ZnSb15 compound was investigated by Sologub et al. (1996b) by the X-ray powder diffraction. It was found to crystallize with the La6 MnSb15 structure type, a = 1.5215, b = 1.9264, c = 0.43215. Sample was synthesized by repeated reaction of sintering of stoichiometric amounts of the starting elements. A proper powder blend was compacted into small pellet, sealed in evacuated quartz tube and slowly heated (within 100 h) to the annealing temperature of 870 K. 3.1.4.12. Ce–Ga–Sb. Mills and Mar (2000) investigated the crystal structure of the Ce12 Ga4 Sb23 compound, with the Pr12 Ga4 Sb23 type structure, a = 0.4308, b = 1.9509, c = 2.6667 (X-ray powder diffraction). The sample was synthesized by a direct reaction of the elements in evacuated silica tubes.

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Fig. 8. Ce–Ge–Sb, isothermal section at 870 K.

3.1.4.13. Ce–Ge–Sb. The isothermal section of the Ce–Ge–Sb phase diagram (ﬁg. 8) was constructed by X-ray analysis of 50 alloys prepared by arc melting in an argon atmosphere and annealed in quartz ampoules under vacuum at 670 K for 500 h (Stetskiv et al., 1998). The purity of the starting metals was better than 99.9 at.%. Three ternary compounds Ce2 GeSb3 (1), ∼Ce5 Ge3 Sb2 (2) and Ce3 GeSb (3) were found. Ce2 GeSb3 is a superstructure of the ThGe2 type structure, a = 1.8894, b = 0.4650, c = 0.4299; Ce3 GeSb crystallizes in the La3 GeIn type structure, a = 1.2012, c = 1.5485; the crystal structure of the ∼Ce5 Ge3 Sb2 is unknown (Stetskiv et al., 1998). One more compound was found and investigated by Lam et al. (2000) from X-ray powder diffraction: Ce6 Ge5−x Sb11+x , a = 0.42972, b = 1.0740, c = 2.6791. 3.1.4.14. Ce–As–Sb. The compounds CeAsx Sb1−x , NaCl type, were synthesized and investigated by different groups of authors: Ce50 As10 Sb40 , a = 0.6354 (Burlet et al., 1980); Ce3 AsSb2 , a = 0.61865 (Ott et al., 1978); Ce4 As0.8 Sb3.2, a = 0.6363 (Rossat-Mignod et al., 1983). 3.1.4.15. Ce–Se–Sb. A complete c–T diagram was presented for the Ce2 Se3 –Sb2 Se3 section by Aliev et al. (1977). CeSe30 Sb19 was found to form a S3 Sb2 structure type, a = 1.159, b = 0.412, c = 1.183. A homogeneity ﬁeld was observed for the (Cex Sb1−x )2 Se3 , x = 0– 0.05, a = 1.162–1.159, b = 0.396–0.412, c = 1.177–1.183. The sample was annealed at 723– 773 K for 300 h. 3.1.4.16. Ce–Zr, Nb–Sb. The compounds Ce3 ZrSb5 and Ce3 NbSb5 belong to the Hf5 CuSn3 anti-type. The lattice parameters are a = 0.9506, c = 0.6318, and a = 0.9438, c = 0.6219 respectively (Bollore et al., 1995; X-ray powder diffraction).

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3.1.4.17. Ce–Ru–Sb. The crystal structure of the CeRu4 Sb12 compound was investigated by Braun and Jeitschko (1980). It was found to crystallize with the LaFe4 P12 type structure, a = 0.92657 (X-ray powder diffraction). The purities of starting materials and experimental procedure were the same as for LaFe4 Sb12 . 3.1.4.18. Ce–Rh–Sb. Malik and Adroja (1991b) observed a KHg2 type with a = 0.4609, b = 0.7416, c = 0.7846 for the CeRhSb compound using X-ray powder diffraction of an arc melted alloy. The purities of the metals were better than 99.99%. Salamakha et al. (2000) reinvestigated the crystal structure of the CeRhSb compound, and found it had the TiNiSi structure type, a = 0.74150, b = 0.46185, c = 0.78570. The existence of CeRh2 Sb2 with a tetragonal structure was reported by Menon Latica and Malik (1996). The Y3 Au3 Sb4 structure type has been reported for the Ce3 Rh3 Sb4 compound by Patil et al. (1998). 3.1.4.19. Ce–Pd–Sb. Marazza et al. (1980) established the CaIn2 type structure with a = 0.4595, c = 0.7894 for the CePdSb compound using X-ray powder diffraction and metallographic analyses. For sample preparation and purity of starting components, see Y–Pd–Sb system. Malik and Adroja (1991a) conﬁrmed the crystal structure and lattice parameters, a = 0.4594, c = 0.7913 (X-ray diffraction; arc melted alloy). CePdSb2 was found to adopt a HfCuSi2 type with the lattice parameters as a = 0.44899, c = 0.9893 (Sologub et al., 1994). For experimental details, see LaNiSb2 . Hoffman and Jeitschko (1985) reported the CaBe2 Ge2 type structure for CePd2 Sb2 , a = 0.4505, c = 1.0230, X-ray powder diffraction. The sample was synthesized in the same manner as LaPd2 Sb2 . The same structure type however with different lattice parameters values, i.e., a = 0.4482, c = 0.9860 was reported for the CePdSb3 sample by Cava et al. (1993). A new ternary antimonide, Ce3 Pd6 Sb5 was prepared by arc melting of the elemental components and subsequent annealing at 1023 K by Gordon et al. (1995). Its orthorhombic crystal structure was determined from single crystal X-ray data: a = 1.3481, b = 0.4459, c = 1.0050. Purity of the elements was at least 99.9%. Crystal structure of two ternary compounds Ce8 Pd24 Sb and Ce2 Pd9 Sb3 was studied by Gordon and DiSalvo (1996) and Gordon et al. (1996) respectively: Ce8 Pd24 Sb, own structure type, space group Pm3m, a = 0.8461 and Ce2 Pd9 Sb3 , own structure type, space group Cmcm, a = 1.3769, b = 0.80412, c = 0.93482 (X-ray single crystal diffraction). 3.1.4.20. Ce–Ag–Sb. The CeAgSb2 compound was observed and studied by Sologub et al. (1995a). It was found to crystallize with HfCuSi2 type structure with the lattice parameters as follows a = 0.43641, c = 1.0722 by X-ray single crystal diffraction of an arc melted and annealed at 870 K for 14 days sample. The purity of starting materials was 99.9 wt.%. The existence and crystal structure of CeAgSb2 compound were independently conﬁrmed by Brylak et al. (1995) (a = 0.4363, c = 1.0699; X-ray single crystal method). A single crystal was obtained by reaction of the elemental components in a NaCl/KCl ﬂux. The starting ratio was Ce:Ag:Sb:NaCl/KCl = 1:1:2:20. The sample was annealed for 2 weeks at 1070 K, cooled to

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960 K at a rate of 3 ◦ C/hr, and quenched in ice water. The NaCl/KCl ﬂux was dissolved in H2 O using an ultrasonic bath. The starting metals were Ce 99.9%, Ag M3N, and Sb 325 mesh, M2N5. 3.1.4.21. Ce–Cd–Sb. Sologub et al. (1995b) reported the crystallographic data for the CeCdSb2 compound (HfCuSi2 type structure, a = 0.43751, c = 1.0900; X-ray powder diffraction) which had been obtained from a multiphase alloy. For sample preparation and purity of starting materials, see CeZn1−x Sb2 . Wollesen et al. (1996) conﬁrmed the crystal structure using X-ray powder diffraction: a = 0.43761, c = 1.0912 for CeCd1−x Sb2 . For experimental details, see LaMn0.721(1)Sb2 . The purities of the starting elements were Ce, greater than 99.9%, Cd, greater than 99.8%, Sb 99.9%. 3.1.4.22. Ce–In–Sb. The crystal structure of the CeIn0.8Sb2 compound (LaIn0.8Sb2 structure type, a = 0.4478, b = 0.4323, c = 1.1796, β = 99.36◦) was investigated by Ferguson et al. (1999) from X-ray powder diffraction. 3.1.4.23. Ce–Sn–Sb. Ferguson et al. (1996) studied the crystal structure of the CeSnx Sb2 by powder diffraction, LaSnSb2 structure type, a = 0.4228, b = 2.2868, c = 0.4478. The sample has been synthesized through direct reaction of the elements at 1223 K. 3.1.4.24. Ce–Te–Sb. The formation and crystal structure of CeTex Sb1−x was studied by Ravot et al. (1982) and Rossat-Mignod et al. (1983) from the samples obtained by heating in molybdenum crucibles at 2273 K and slow cooling: NaCl structure type, x = 0–0.5, a = 0.6422–0.6403. Charvillat et al. (1977) established the Cu2 Sb structure type for the CeSbTe compound, a = 0.4365, c = 0.945. 3.1.4.25. Ce–Hf–Sb. The crystal structure of the Ce3 HfSb5 compound was determined by Bollore et al. (1995). It was found to adopt the Hf5 CuSn3 anti-type structure, a = 0.9483, c = 0.6298 (X-ray powder diffraction). 3.1.4.26. Ce–Os–Sb. The crystal structure of the CeOs4 Sb12 compound was investigated by Braun and Jeitschko (1980). It forms the LaFe4 P12 type structure, a = 0.93011 (X-ray powder diffraction). The purities of starting materials and experimental procedure were the same as for LaFe4 Sb12 . 3.1.4.27. Ce–Pt–Sb. CePtSb belongs to the CaIn2 type structure, a = 0.4550, c = 0.8077 (powder diffraction; Rossi et al., 1981). The alloy was melted in an induction furnace under argon in tantalum crucible, annealed at 773 for 1 week. The purity of starting materials was Ce (3N), Pt and Sb (4N) each. Kasaya et al. (1991) reported the Y3 Au3 Sb4 type structure for the compound Ce3 Pt3 Sb4 , a = 0.9820 (powder diffraction; arc melted alloy).

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3.1.4.28. Ce–Au–Sb. The HfCuSi2 type structure with the lattice parameters as a = 0.44081, c = 1.0339 was reported for the CeAuSb2 compound (Sologub et al., 1994). The alloy was prepared by argon arc melting ingots of the elements with the nominal composition Ce25 Au25Sb50 and annealed at 670 K in evacuated quartz tubes for 2 weeks and quenched in water. The materials used were Ce 99.9%, Au 99.9%, and Sb 99.9%. Wollesen et al. (1996) conﬁrmed the crystal structure using X-ray powder diffraction: a = 0.4381, c = 1.0772 for CeAuSb2 . The sample was prepared by annealing cold-pressed and arc melted mixtures of starting materials taken with the atomic ratio 1:1:2 in evacuated sealed silica tubes for 10 days at 1070 K followed by cooling at a rate of 100 ◦ C/h. The purities of starting elements were Ce, greater than 99.9%, Au, greater than 99.9%, Sb 99.9%. CeAuSb crystallizes with CaIn2 type structure, a = 0.4616, c = 0.8322 after Suzuki et al. (1993) from powder diffraction of arc melted and annealed at 1273 K for 48 h alloy. Kasaya et al. (1991) reported a Y3 Au3 Sb4 type structure for the compound Ce3 Au3 Sb4 , a = 1.0058 (powder diffraction; powder metallurgical technique). The formation and crystal structure of this compound (Y3 Au3 Sb4 type, a = 1.00443) was conﬁrmed by Sologub et al. (1998) from X-ray powder diffraction of arc melted and annealed at 1070 K for two weeks alloys. 3.1.5. Pr–M–Sb systems 3.1.5.1. Pr–Li–Sb. The formation of one ternary compound was reported by Fischer and Schuster (1982): PrLi2 Sb2 , CaBe2 Ge2 type structure, a = 0.4329, c = 1.0990 (X-ray single crystal data). The alloy was prepared by heating the elements in a Ta crucible at 870–1170 K for 24–48 h. 3.1.5.2. Pr–Ti–Sb. Bollore et al. (1995) investigated the crystal structure of the Pr3 TiSb5 compound by X-ray powder diffraction. It crystallizes with the Hf5 CuSn3 anti-type structure, a = 0.9401, c = 0.6224. 3.1.5.3. Pr–V–Sb. PrVSb3 has the CeCrSb3 structure type structure, a = 1.3121, b = 0.62380, c = 0.60182 (X-ray powder diffraction; Brylak and Jeitschko, 1995). 3.1.5.4. Pr–Cr–Sb. PrCrSb3 crystallizes with the CeCrSb3 type structure: a = 1.3043, b = 0.618831, c = 0.60738 (X-ray powder diffraction; Brylak and Jeitschko, 1995). The crystal structure was conﬁrmed by Ferguson et al. (1997) a = 1.3127, b = 0.6199, c = 0.6092 (X-ray powder diffraction). 3.1.5.5. Pr–Mn–Sb. Sologub et al. (1995b) reported the lattice parameters for PrMn0.82Sb2 (HfCuSi2 -type, a = 0.43362, c = 1.0628; X-ray powder diffraction) obtained from a multiphase alloy. For experimental details, see LaMn0.87Sb2 . Wollesen et al. (1996) conﬁrmed the crystal structure using X-ray powder diffraction: a = 0.4333, c = 1.0627 for PrMn1−x Sb2 . For experimental details, see LaMn0.721(1)Sb2 . The purities of the starting elements were Pr, greater than 99.9%, Mn, greater than 99.8%, Sb 99.9%.

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3.1.5.6. Pr–Fe–Sb. Leithe-Jasper and Rogl (1994) investigated the formation and crystal structure of the PrFe1−x Sb2 compound by X-ray powder analysis of the alloy Pr30−30.5Fe13−14.5 Sb57−55 (HfCuSi2 type structure, a = 0.43638–0.43616, c = 0.97390– 0.97552). For sample preparation and purity of starting materials, see LaFe1−x Sb2 . The crystal structure of the PrFe4 Sb12 compound was studied by Braun and Jeitschko (1980). It was found to form the LaFe4 P12 type structure, a = 0.91351 (X-ray powder diffraction). The purities of starting materials and experimental procedure were the same as for LaFe4 Sb12. From room temperature X-ray powder diffraction analysis the Pr6 Fe13 Sb was found to crystallize with the ordered La6 Co11 Ga3 , i.e., the Nd6 Fe13 Si type, a = 0.8108, c = 2.3303 (Weitzer et al., 1993). An alloy was synthesized from ingots and compacted powders of the constituent elements, 99.9% pure, by arc melting, followed by annealing at 1273 for 2 days and quenched in cold water. 3.1.5.7. Pr–Co–Sb. Leithe-Jasper and Rogl (1994) investigated the formation and crystal structure of the PrCo1−x Sb2 compound by X-ray powder analysis of the alloy Pr28 Co17 Sb55 (HfCuSi2 -type structure, a = 0.43415, c = 0.96700). For sample preparation and purity of starting materials, see LaFe1−x Sb2 . Wollesen et al. (1996) conﬁrmed the crystal structure using X-ray powder diffraction: a = 0.43463, c = 0.9694 for PrCo1−x Sb2 . For synthesis, see LaMn0.721(1)Sb2 . The purities of the starting elements were Pr, greater than 99.9%, Co, greater than 99.8%, Sb 99.9%. 3.1.5.8. Pr–Ni–Sb. Pankevich et al. (1983) reported the crystal structure for the PrNiSb2 compound to have the HfCuSi2 type structure, a = 0.4379, c = 0.9672 (X-ray powder diffraction; arc melted and annealed at 870 K for two weeks alloy). The crystallographic characteristics were conﬁrmed by Sologub et al. (1994), a = 0.43853, c = 0.9699. For experimental details, see LaNiSb2 . Early investigations of the PrNiSb compound showed that it had the AlB2 -type structure with a = 0.4376, c = 0.4053 (Pecharsky et al., 1983a; X-ray powder analysis). For experimental procedure, see ScNiSb. At variance with these data, Hartjes and Jeitschko (1995) suggested a ZrBeSi type structure, a = 0.4375, c = 0.8123 from X-ray powder diffraction. For experimental details, see LaNiSb. The CeGa2 Al2 type structure was announced for PrNi2 Sb2 compound by Pecharsky et al. (1982), a = 0.4367, c = 0.9904 from X-ray powder diffraction. For sample preparation, see CeNi2 Sb2 . Hoffman and Jeitschko (1988) established the defect CaBe2 Ge2 type structure for PrNi2−x Sb2 , a = 0.4399, c = 0.9778, X-ray powder diffraction. For the experimental details, see CeNi2−x Sb2 . CaBe2 Ge2 type structure was conﬁrmed from an arc melted alloy PrNi2 Sb2 : a = 0.4360, c = 0.9970; a monoclinic distortion was observed after annealing at 1070 K for one week: a = 0.4365, b = 0.4355, c = 0.9969, β = 90.20◦ (X-ray powder diffraction; Slebarski et al., 1996). 3.1.5.9. Pr–Cu–Sb. A ternary compound of praseodymium with copper and antimony of the stoichiometric ratio 3:3:4 was identiﬁed and studied by means of X-ray analysis by Skolozdra

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et al. (1993). Pr3 Cu3 Sb4 compound was found to have the Y3 Au3 Sb4 type structure with the lattice parameter of a = 0.9695 (X-ray powder diffraction). For experimental details, see the Y–Cu–Sb system. PrCuSb2 was found to form the HfCuSi2 type structure with the lattice parameters of a = 0.43250, c = 1.0159 (Sologub et al., 1994). For experimental details, see LaNiSb2 . The CaBe2 Ge2 type structure was established for PrCu2 Sb2 from an arc melted alloy: a = 0.4329, c = 1.0183 (X-ray powder diffraction; Slebarski et al., 1996). 3.1.5.10. Pr–Zn–Sb. Sologub et al. (1995b) reported on the crystallographic data for the PrZn1−x Sb2 compound (HfCuSi2 type structure, a = 0.43398, c = 1.0373; X-ray powder diffraction) obtained from a multiphase alloy. For the sample preparation and the purity of the starting materials, see CeZn1−x Sb2 . Wollesen et al. (1996) conﬁrmed the crystal structure by using X-ray powder diffraction: a = 0.43400, c = 1.0358 for PrZn1−x Sb2 . For experimental details, see LaMn0.721(1)Sb2 . The purities of the starting elements were Pr, greater than 99.9%, Zn, greater than 99.8%, Sb 99.9%. The crystal structure of the Pr6 ZnSb15 compound was investigated by Sologub et al. (1996b) by X-ray powder diffraction. It was found to crystallize with the La6 MnSb15 structure type, a = 1.5136, b = 1.9180, c = 0.42898. For sample preparation, see Ce6 ZnSb15. 3.1.5.11. Pr–Ga–Sb. Mills and Mar (2000) studied the crystal structure of Pr12 Ga4 Sb23 by X-ray single crystal diffraction. This compound has its own structure type, space group Immm, a = 0.4283, b = 1.9394, c = 2.6553. The crystal was obtained from the sample synthesized through the direct reaction of the elements in evacuated silica tubes. 3.1.5.12. Pr–Ge–Sb. The Pr6 Ge5−x Sb11+x compound was observed and investigated by Lam et al. (2001) using X-ray powder diffraction and found that it had the La6 Ge2.8 Sb13.2 structure type, a = 0.42674, b = 1.0677, c = 2.6626. 3.1.5.13. Pr–Zr, Nb–Sb. The Pr3 ZrSb5 and Pr3 NbSb5 compounds belong to the Hf5 CuSn3 anti-type structure with lattice parameters of a = 0.9450, c = 0.6293 and a = 0.9396, c = 0.6201 respectively (Bollore et al., 1995; X-ray powder diffraction). 3.1.5.14. Pr–Ru–Sb. Braun and Jeitschko (1980) reported the crystal structure of the PrRu4 Sb12 compound to be of the LaFe4 P12 type structure, a = 0.92648 (X-ray powder diffraction). The purities of starting materials and experimental procedure were the same as for LaFe4 Sb12 . 3.1.5.15. Pr–Rh–Sb. Malik and Adroja (1991b) established a KHg2 type with a = 0.4596, b = 0.7391, c = 0.7848 for the PrRhSb compound by using X-ray powder diffraction of an arc melted alloy. The purities of the metals were better than 99.99%. Adroja et al. (1999) observed the TiNiSi structure type for the PrRhSb0.976 compound from metallographic analyses and powder diffraction.

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The existence of PrRh2 Sb2 with a tetragonal structure was reported by Menon Latica and Malik (1996). 3.1.5.16. Pr–Pd–Sb. Marazza et al. (1980) reported the CaIn2 type structure with a = 0.4593, c = 0.7805 for the PrPdSb compound from X-ray powder diffraction and metallographic analyses. For the sample preparation and the purity of starting components, see Y–Pd–Sb system. The crystallographic characteristics were also conﬁrmed from powder diffraction data of arc melted and annealed at 1073 K alloys (Zygmunt and Szytula, 1995): CaIn2 type structure, a = 0.4588, c = 0.7836. Adroja et al. (1999) observed a LiGaGe structure type for the PrPdSb0.952 compound from metallographic analyses and powder diffraction. PrPdSb2 was found to adopt the HfCuSi2 type structure with the lattice parameters as a = 0.44707, c = 0.9790 (Sologub et al., 1994). For experimental details, see LaNiSb2 . Hoffman and Jeitschko (1988) established a CaBe2 Ge2 structure for PrPd2 Sb2 alloy, X-ray powder diffraction. Sample was synthesized in the same manner as LaPd2 Sb2 . 3.1.5.17. Pr–Ag–Sb. The PrAgSb2 compound was observed and studied by Sologub et al. (1995a). It was found to crystallize with HfCuSi2 type structure with lattice parameters as follows a = 0.43506, c = 1.0679 by X-ray powder diffraction of arc melted and annealed at 870 K for 14 days alloy. The purity of starting materials was 99.9 wt.%. The existence and crystal structure of PrAgSb2 were independently conﬁrmed by Brylak et al. (1995) (a = 0.43499, c = 1.0670; X-ray powder diffraction). For sample preparation, see YAgSb2 . The starting materials purities were Pr 99.9%, Ag M3N, and Sb 325 mesh, M2N5. 3.1.5.18. Pr–Cd–Sb. Sologub et al. (1995b) reported on the crystallographic data for the PrCdSb2 compound (HfCuSi2 type structure, a = 0.43574, c = 1.0864; X-ray powder diffraction) obtained from a multiphase alloy. For the sample preparation and the purity of the starting materials, see CeZn1−x Sb2 . Wollesen et al. (1996) conﬁrmed the crystal structure using X-ray powder diffraction: a = 0.43588, c = 1.08555 for PrCd1−x Sb2 . For experimental details, see LaMn0.721(1)Sb2 . The purities of the starting elements were Pr, greater than 99.9%, Cd, greater than 99.8%, Sb 99.9%. 3.1.5.19. Pr–In–Sb. The crystal structure of the PrIn0.8Sb2 (LaIn0.8Sb2 structure type, a = 0.4465, b = 0.4303, c = 1.1733, β = 99.45◦) was investigated by Ferguson et al. (1999) by using X-ray powder diffraction. 3.1.5.20. Pr–Sn–Sb. Ferguson et al. (1996) investigated the crystal structure of the PrSnx Sb2 compound by X-ray powder diffraction: LaSnSb2 structure type, a = 0.4204, b = 2.2700, c = 0.4469. The sample was synthesized by direct reaction of the elements at 1223 K. 3.1.5.21. Pr–Te–Sb. Charvillat et al. (1977) reported a Cu2 Sb structure type for the PrTeSb compound, a = 0.4344, c = 0.9396.

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3.1.5.22. Pr–Hf–Sb. The crystal structure of the Pr3 HfSb5 compound was studied by Bollore et al. (1995). It was found to form the Hf5 CuSn3 anti-type, a = 0.9419, c = 0.6271 (X-ray powder diffraction). 3.1.5.23. Pr–Os–Sb. The crystal structure of the PrOs4 Sb12 compound was investigated by Braun and Jeitschko (1980). It belongs to the LaFe4 P12 type structure, a = 0.92994 (X-ray powder diffraction). The purities of the starting materials and the experimental procedure were the same as for LaFe4 Sb12 . 3.1.5.24. Pr–Pt–Sb. Wenski and Mewis (1986a) reported the LiGaGe type structure for the PrPtSb compound, a = 4537, c = 0.7963 from X-ray powder diffraction. The sample was arc melted and annealed at 1273–1373 K for 3–4 weeks. The starting components were Pr (3N), Pt (3N), Sb (3N). Kasaya et al. (1991) observed the Y3 Au3 Sb4 type structure for the compound Pr3 Pt3 Sb4 , a = 0.9981 (powder diffraction; arc melted alloy). 3.1.5.25. Pr–Au–Sb. PrAuSb2 was found to adopt a HfCuSi2 type structure with the lattice parameters as a = 0.43933, c = 1.0290 (Sologub et al., 1994). The alloy was prepared in the same manner as YCuSb2 . Kasaya et al. (1991) reported the Y3 Au3 Sb4 type structure for the compound Pr3 Au3 Sb4 , a = 1.0013 (powder diffraction; powder metallurgical technique). 3.1.6. Nd–M–Sb systems 3.1.6.1. Nd–Li–Sb. No ternary phase diagram exists for the Nd–Li–Sb system, however the formation of one ternary compound has been reported by Fischer and Schuster (1982): NdLi2 Sb2 with the CaBe2 Ge2 type structure, a = 0.4280, c = 1.0910 (X-ray single crystal data). The alloy was prepared by heating the elements in a Ta crucible at 870–1170 K for 24–48 h. 3.1.6.2. Nd–Ti–Sb. The crystal structure of the Nd3 TiSb5 compound was investigated by Bollore et al. (1995). It was found to form the Hf5 CuSn3 anti-type structure, a = 0.9353, c = 0.6196 (X-ray powder diffraction). 3.1.6.3. Nd–V–Sb. The only information available on the interaction of the components in the Nd–V–Sb system is the formation of the NdVSb3 compound observed by Brylak and Jeitschko (1995). It was reported to adopt the CeCrSb3 type structure, a = 1.3040, b = 0.6226, c = 0.6008 from X-ray powder diffraction. 3.1.6.4. Nd–Cr–Sb. The partial isothermal section of the Nd–Cr–Sb system (33.0–100.0 at.% Sb) at 870 K was constructed by Sologub and Salamakha (1999) (ﬁg. 9). The formation and crystal structure of one ternary compound NdCrSb3 (1) has been conﬁrmed: CeCrSb3 type structure, a = 1.2970, b = 0.61679, c = 0.60592 (Brylak and Jeitschko, 1995 and Ferguson

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Fig. 9. Nd–Cr–Sb, partial isothermal section at 870 K (33.0–100.0 at.% Sb).

et al., 1997). The solubility of third component in the binary compounds was found to be negligible. The ternary samples used to derive the phase relations in the ternary sections at 870 K, each weighting 1 g, were synthesized by arc melting the proper amounts of the constituent elements under high purity argon on a water cooled copper hearth. The starting materials were used in the form of ingots of high purity elements – Nd (99.9%), Cr (99.99%), Sb (99.999%). The alloys were annealed at 870 K in evacuated quartz tubes for 2 weeks and quenched in water. 3.1.6.5. Nd–Mn–Sb. Phase equilibria were established in the Nd–Mn–Sb ternary system for an isothermal section at 870 K by Sologub et al. (1996a) (ﬁg. 10). Three ternary compounds were observed: ∼Nd26Mn8 Sb66 (1) (type unknown), Nd29 Mn13Sb58 (2) (type unknown) and NdMn1−x Sb2 , x = ∼0.15 (3). For the sample preparation, see Ce–Mn–Sb system. Sologub et al. (1995b) reported on the crystal structure for the NdMn0.83Sb2 compound (HfCuSi2 type structure, a = 0.43097, c = 1.0672; X-ray powder diffraction). For experimental details, see LaMn0.87Sb2 . Wollesen et al. (1996) conﬁrmed the crystal structure using X-ray powder diffraction: a = 0.43174, c = 1.0599 for NdMn1−x Sb2 . For experimental details, see LaMn0.721(1)Sb2 . The purities of the starting elements were: Nd, greater than 99.9%, Mn, greater than 99.8%, Sb 99.9%. 3.1.6.6. Nd–Fe–Sb. Two ternary compounds (NdFe4 Sb12 (1) and NdFe1−x Sb2 (2) have been observed as a result of X-ray phase analyses of 30 ternary neodymium–iron–antimony alloys within the concentration region 33.0–100.0 at.% Sb at 870 K (ﬁg. 11) (Sologub and Salamakha, 1999). The solubilities of third component in the binary compounds were found to be negligible. A small homogeneity range was observed for the NdFe1−x Sb2 compound. For the sample preparation, see Nd–Cr–Sb system. The starting materials were used in the form of ingots of high purity elements – Nd (99.9%), Fe (99.99%), Sb (99.999%).

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Fig. 10. Nd–Mn–Sb, isothermal section at 870 K.

Fig. 11. Nd–Fe–Sb, partial isothermal section at 870 K (33.0–100.0 at.% Sb).

Leithe-Jasper and Rogl (1994) investigated the formation and crystal structure of the NdFe1−x Sb 2 compound by X-ray powder analysis of the alloy Nd31−32 Fe14−13Sb57−55 (HfCuSi2 type structure, a = 0.43457–0.43479, c = 0.96405–0.96554). These results were conﬁrmed by the same authors using X-ray single crystal analysis: NdFe0.6 Sb2 , HfCuSi2 type structure, a = 0.43514, c = 0.96518. For the sample preparation and the purity of starting materials, see LaFe1−x Sb2 .

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The crystal structure of the NdFe4 Sb12 compound was studied Evers et al. (1995). It was found to adopt the LaFe4 P12 type structure, a = 0.9130 (X-ray powder and single crystal diffraction). The purities of the materials were 99.9% or better. Filings of the neodymium were prepared under argon and annealed with the corresponding amounts of antimony in evacuated sealed silica tubes for two days at 723 K, followed by ﬁve days at 1023 K. The resulting antimonide NdSb was ground together with appropriate amounts of Fe and Sb, pressed into pellets and sealed in evacuated silica tubes. The ampules were quickly heated to 933 K, kept at this temperature for 3 h, cooled at 1 ◦ C/h to 873 K and then quenched. The starting composition was Nd:Fe:Sb = 2:4:13. The excess antimony was removed by treating the product for several days with concentrated hydrochloric acid. From room temperature X-ray powder diffraction analysis Nd6 Fe13 Sb was found to crystallize with the ordered La6 Co11 Ga3 , i.e., the Nd6 Fe13 Si type structure, a = 0.8098, c = 2.3232 (Weitzer et al., 1993). An alloy was synthesized from ingots and compacted powders of the constituent elements, 99.9% pure, by arc melting, followed by annealing at 1073 for 7 days and quenched in cold water. Leithe-Jasper (1994) reported the single crystal investigations for two compounds with unique structure types: NdFe3 Sb2 , a = 0.42879, c = 2.57048 and NdFe2−x Sb2 , a = 0.42965, b = 0.42759, c = 2.57887. Zhang et al. (2000) reported that the Nd2 Fe17 binary compound dissolves about 3 at.% of Sb at 1223 K. 3.1.6.7. Nd–Co–Sb. The 870 K isothermal section of the Nd–Co–Sb system was reported by Sologub and Salamakha (1999) from an X-ray powder analysis of 68 alloys (ﬁg. 12). For the sample preparation, see Nd–Cr–Sb system. The purity of the starting components

Fig. 12. Nd–Co–Sb, isothermal section at 870 K.

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Fig. 13. Nd–Ni–Sb, isothermal section at 870 K.

was Nd 99.9%, Co 99.99%, and Sb 99.999%. The existence of the ternary NdCo1−x Sb2 (3) phase has been conﬁrmed. The crystal structures of two other compounds, NdCo3 Sb2 (1) and Nd6 CoSb15 (2) have not been investigated. Leithe-Jasper and Rogl (1994) investigated the formation and crystal structure of the NdCo1−x Sb2 compound by X-ray powder analysis of Nd30−25Co15−25 Sb55−50 (HfCuSi2 type structure, a = 0.43306–0.43453, c = 0.96138–0.96918). For the sample preparation and the purity of the starting materials, see LaFe1−x Sb2 . Wollesen et al. (1996) conﬁrmed the crystal structure using X-ray powder diffraction: a = 0.43357, c = 0.96587 for NdCo1−x Sb2 . For synthesis, see LaMn0.721(1)Sb2 . The purities of the starting elements were: Nd, greater than 99.9%, Co, greater than 99.8%, Sb 99.9%. 3.1.6.8. Nd–Ni–Sb. The isothermal section of the Nd–Ni–Sb system at 870 K is shown in ﬁg. 13, after Salamakha (1998). Three ternary compounds have been found: NdNi2 Sb2 (1), NdNiSb2 (2) and NdNiSb (3). The solubility of third component in the binary compounds was found to be negligible. For the sample preparation, see Nd–Cr–Sb system. The purity of the starting components was: Nd 99.9%, Ni 99.99%, and Sb 99.999%. Pankevich et al. (1983) reported the crystal structure of NdNiSb2 to be the HfCuSi2 type, a = 0.4364, c = 0.9614 (X-ray powder diffraction; arc melted and annealed at 870 K for two weeks). The crystallographic characteristics were conﬁrmed by Sologub et al. (1994), a = 0.43674, c = 0.9629. For experimental details, see LaNiSb2 . Early investigations of the NdNiSb compound showed that it had the AlB2 -type with a = 0.4372, c = 0.3991 (Pecharsky et al., 1983a; X-ray powder analysis). For the experimental procedure, see ScNiSb. At variance with these data, Hartjes and Jeitschko (1995) suggested

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Fig. 14. Nd–Cu–Sb, isothermal section at 870 K.

that the compound had the ZrBeSi type structure, a = 0.4377, c = 0.7997 from X-ray powder diffraction. For experimental details, see LaNiSb. The CeGa2 Al2 type structure was reported for NdNi2 Sb2 by Pecharsky et al. (1982), a = 0.43022, c = 0.99125 from X-ray powder diffraction. For sample preparation, see CeNi2 Sb2 . Hoffman and Jeitschko (1988) established a defect CaBe2 Ge2 type structure for NdNi2−x Sb2 alloy, a = 0.4300, c = 1.001, X-ray powder diffraction. For the experimental details, see CeNi2−x Sb2 . 3.1.6.9. Nd–Cu–Sb. The isothermal section for the Nd–Cu–Sb system at 870 K was established by Zaplatynsky and Salamakha (1994) (ﬁg. 14). For sample preparation, see Nd–Cr–Sb. The purity of the starting components was: Nd 99.9%, Ni 99.99%, and Sb 99.999%. Three ternary compounds were found to exist. No homogeneous ranges were encountered for the ternary compounds. A ternary compound of neodymium with copper and antimony of the stoichiometric ratio 3:3:4 was identiﬁed and studied by means of X-ray analysis by Skolozdra et al. (1993). The Nd3 Cu3 Sb4 compound (3) was found to have the Y3 Au3 Sb4 type structure with a lattice parameter of a = 0.9661 (X-ray powder diffraction). For experimental details, see the Y–Cu– Sb system. NdCuSb2 (2) was found to adopt a HfCuSi2 type structure with lattice parameters of a = 0.43118, c = 1.0111 (Sologub et al., 1994). For experimental details, see LaNiSb2 . Crystal structure of the compound NdCu6 Sb3 (1) has not been investigated. 3.1.6.10. Nd–Zn–Sb. The results of an X-ray phase analysis of 25 ternary neodymium-zincantimony alloys for the Sb-rich region (33.0–100.0 at.% of Sb) are presented in ﬁg. 15 (Sologub and Salamakha, 1999). The alloys were obtained via a powder metallurgical reaction,

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Fig. 15. Nd–Zn–Sb, partial isothermal section at 870 K (33.0–100.0 at.% Sb).

the sintering of Zn and Sb powders with ﬁne ﬁlings of neodymium. The thoroughly mixed blends were compacted in the steel dies and then sealed in evacuated silica ampoules. After slowly heating to about 870 K for the ﬁrst reaction, the hard sintered pellets were reground under C6 H12 and recompacted for the ﬁnal heat treatment at 870 K for 300 h and ﬁnally quenched by submerging the silica capsules in cold water. Phase ﬁeld distribution is characterized by the existence of three ternary compounds. The obtained data on formation and crystal structure of two compounds NdZn1−x Sb2 (2) (HfCuSi2 type structure, a = 0.43305, c = 1.03482, X-ray powder diffraction) and Nd6 ZnSb15 (3) (La6 MnSb15 type, a = 1.5109, b = 1.9026, c = 0.42447, X-ray powder diffraction) are in good agreement with the results of former investigations (Sologub et al., 1995b; Sologub et al., 1996b). Wollesen et al. (1996) conﬁrmed the crystal structure for the NdZn1−x Sb2 (a = 0.43229, c = 1.03334) from the X-ray powder diffraction. The purity of the starting components and the sample preparation procedure were the same as for LaMn0.721(1)Sb2 . The crystal structure of the ∼NdZn2Sb2 (1) ternary phase has not been determined yet (Sologub and Salamakha, 1999). 3.1.6.11. Nd–Ga–Sb. Mills and Mar (2000) investigated by X-ray powder diffraction the crystal structure of the Nd12Ga4 Sb23 compound, Pr12 Ga4 Sb23 type structure, a = 0.4268, b = 1.308, c = 2.6425. The sample was synthesized by direct reaction of the elements in evacuated silica tubes. 3.1.6.12. Nd–Ge–Sb. Lam et al. (2001) determined the crystal structure of the Nd6 Ge3.6Sb12.4 compound from X-ray single crystal diffraction, La6 Ge2.8 Sb13.2 structure type, a = 0.4210, b = 1.06362, c = 2.6536. The crystal was obtained from a sample synthesized by direct reaction of the elements at 1223 K.

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3.1.6.13. Nd–Zr, Nb–Sb. The compounds Nd3 ZrSb5 and Nd3 NbSb5 belong to the Hf5 CuSn3 anti-type structure with the lattice parameters a = 0.9413, c = 0.6275, and a = 0.9360, c = 0.6186, respectively (Bollore et al., 1995; X-ray powder diffraction). 3.1.6.14. Nd–Ru–Sb. The crystal structure of the NdRu4 Sb12 compound was investigated by Braun and Jeitschko (1980). It was found to form the LaFe4 P12 type, a = 0.92642 (X-ray powder diffraction). The purities of the starting materials and the experimental procedure were the same as for LaFe4 Sb12 . 3.1.6.15. Nd–Rh–Ge. Malik and Adroja (1991b) established the KHg2 type structure with a = 0.4584, b = 0.7329, c = 0.7838 for the NdRhSb compound by using X-ray powder diffraction of an arc melted alloy. The purities of the metals were better than 99.99%. The existence of NdRh2 Sb2 with a tetragonal structure was reported by Menon Latica and Malik (1996). 3.1.6.16. Nd–Pd–Sb. Marazza et al. (1980) established the CaIn2 type structure with a = 0.4580, c = 0.7716 for NdPdSb compound by using X-ray powder diffraction and metallographic analyses. For the sample preparation and the purity of starting components, see Y–Pd–Sb system. The crystallographic characteristics were conﬁrmed from powder diffraction of arc melted and annealed at 1073 K alloys with a = 0.4577, c = 0.7676 (Zygmunt and Szytula, 1995). Mehta et al. (1995) reported an orthorhombic structure for NdPdSb at room temperature: SG Pmma, a = 0.45833, b = 0.77189, c = 0.7937. NdPdSb2 was found to crystallize with the HfCuSi2 type structure with lattice parameters of a = 0.44647, c = 0.9738 (Sologub et al., 1994). For experimental details, see LaNiSb2 . Hoffman and Jeitschko (1988) established the CaBe2 Ge2 type structure for NdPd2Sb2 , X-ray powder diffraction. The sample was synthesized in the same manner as LaPd2 Sb2 . 3.1.6.17. Nd–Ag–Sb. The isothermal section for the Nd–Ag–Sb system at 870 K was established by Zaplatynsky and Salamakha (1994) (ﬁg. 16). For the sample preparation, see Nd– Cr–Sb. The purity of the starting components was: Nd 99.9%, Ag 99.99%, and Sb 99.999%. One ternary compound NdAgSb2 (1) was found to exist. Its crystal structure was independently investigated by two groups of authors (Sologub et al., 1995a; Brylak et al., 1995). This compound was found to belong to the HfCuSi2 type structure, a = 0.43357, c = 1.0624. The alloys were prepared in the same manner as YAgSb2 . 3.1.6.18. Nd–Cd–Sb. Figure 17 represents the partial isothermal section of the Nd–Cd–Sb system (33.0–100.0 at.% of Sb) at 870 K, after Sologub and Salamakha (1999). For the sample preparation, see Nd–Zn–Sb system. The phase relations are characterized by the existence of three ternary compounds: NdCdSb2 (1), ∼Nd6 CdSb15 (2) and ∼NdCdSb (3). Sologub et al. (1995b) reported on the crystallographic data for the NdCdSb2 (1) compound (HfCuSi2 -type structure, a = 0.43454, c = 1.0827; X-ray powder diffraction) obtained from a multiphase alloy. For the sample preparation and the purity of the starting materials,

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Fig. 16. Nd–Ag–Sb, isothermal section at 870 K.

Fig. 17. Nd–Cd–Sb, partial isothermal section at 870 K (33.0–100.0 at.% Sb).

see CeZn1−x Sb2 . Wollesen et al. (1996) conﬁrmed the crystal structure using X-ray powder diffraction: a = 0.43405, c = 1.0820 for NdCd1−x Sb2 . For experimental details, see LaMn0.721(1)Sb2 . The purities of the starting elements were: Nd, greater than 99.9%, Cd, greater than 99.8%, Sb 99.9%. 3.1.6.19. Nd–In–Sb. The crystal structure of the NdIn0.8Sb2 compound was investigated by Ferguson et al. (1999) using X-ray powder diffraction: LaIn0.8Sb2 structure type, a = 0.4445, b = 0.4297, c = 1.1677, β = 99.22◦. 3.1.6.20. Nd–Sn–Sb. Ferguson et al. (1996) studied the crystal structure of the NdSnx Sb2 by using a powder diffraction method, a = 0.4195, b = 2.2606, c = 0.4449. The sample was synthesized by direct reaction of the elements at 1223 K.

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3.1.6.21. Nd–Te–Sb. The complete c–T diagram was presented for the Nd2 Te3 –Sb2 Te3 section by Geidarova and Rustamov (1985). The NdTe3 Sb compound, which formed incongruently, was observed to have the: Bi2 Te3 structure type, a = 0.432, c = 2.940 (Geidarova and Rustamov, 1985). NdSbTe has the Cu2 Sb type structure, a = 0.4312, c = 0.9371 (Charvillat et al., 1977). 3.1.6.22. Nd–Hf–Sb. Bollore et al. (1995) reported that Nd3 HfSb5 (studied by X-ray powder diffraction) has the Hf5 CuSn3 anti-type structure, a = 0.9390, c = 0.6261. 3.1.6.23. Nd–Os–Sb. The crystal structure of the NdOs4 Sb12 compound was investigated by Braun and Jeitschko (1980). It was found to adopt the LaFe4 P12 type structure, a = 0.92989 (X-ray powder diffraction). The purities of the starting materials and the experimental procedures were the same as for LaFe4 Sb12 . These results were conﬁrmed by Evers et al. (1995), a = 0.9300 from X-ray single crystal analysis. 3.1.6.24. Nd–Pt–Sb. NdPtSb crystallizes with the CaIn2 type structure, a = 0.4544, c = 0.7878 (Rossi et al., 1981; powder X-ray diffraction data). For the experimental details, see the LaPtSb. At variance with these data, Wenski and Mewis (1986a) reported the LiGaGe type structure for the NdPtSb compound, a = 0.4535, c = 0.7866 from X-ray single crystal investigation. For the sample preparation, see PrPtSb. 3.1.6.25. Nd–Au–Sb. The partial isothermal section of the Nd–Au–Sb system (33.0–100.0 at.% of Sb) at 870 K is shown in ﬁg. 18 after Zaplatynsky (2000). Two ternary compounds were found to exist within investigated concentration region. For sample preparation, see Nd– Zn–Sb system.

Fig. 18. Nd–Au–Sb, partial isothermal section at 870 K (33.0–100.0 at.% Sb).

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The Y3 Au3 Sb4 type structure was reported by Dwight (1977) for the Nd3 Au3 Sb4 alloy (2) (a = 0.9961; X-ray powder diffraction). The conditions of synthesis were not speciﬁed. The formation and crystal structure of the Nd3 Au3 Sb4 compound (Y3 Au3 Sb4 type, a = 1.99716) was conﬁrmed by Sologub et al. (1998). For the sample preparation, see Nd3 Au3 Sb4 . NdAuSb2 (1) was found to adopt the HfCuSi2 type structure with the lattice parameters as a = 0.43870, c = 1.0192 (Sologub et al., 1994). The alloy was prepared in the same manner as YCuSb2 . 3.1.7. Sm–M–Sb systems 3.1.7.1. Sm–Ti–Sb. The crystal structure of the Sm3 TiSb5 compound was investigated by Bollore et al. (1995). It was found to form the Hf5 CuSn3 anti-type structure, a = 0.9275, c = 0.6162 (X-ray powder diffraction). 3.1.7.2. Sm–V–Sb. The SmVSb3 compound has the CeCrSb3 type structure: a = 1.2904, b = 0.6213, c = 0.5980 (X-ray powder diffraction; Brylak and Jeitschko, 1995). 3.1.7.3. Sm–Cr–Sb. SmCrSb3 crystallizes with the CeCrSb3 type structure: a = 1.2838, b = 0.61594, c = 0.6032 (X-ray powder diffraction; Brylak and Jeitschko, 1995). The structure was conﬁrmed by Ferguson et al. (1997), a = 1.2847, b = 0.6164, c = 0.6038 (X-ray powder diffraction). 3.1.7.4. Sm–Mn–Sb. Sologub et al. (1995b) reported on the lattice parameters for the SmMn0.90Sb2 compound (HfCuSi2 -type, a = 0.42899, c = 1.0569; X-ray powder diffraction) which was obtained from a multiphase alloy. For experimental details, see LaMn0.87Sb2 . Wollesen et al. (1996) conﬁrmed the crystal structure using X-ray powder diffraction: a = 0.4298, c = 1.0520 for SmMn1−x Sb2 . For experimental details, see LaMn0.721Sb2 . The purities of the starting elements were: Sm, greater than 99.9%, Mn, greater than 99.8%, Sb 99.9%. 3.1.7.5. Sm–Fe–Sb. Leithe-Jasper and Rogl (1994) investigated the formation and crystal structure of the SmFe1−x Sb2 compound by X-ray powder analysis of the alloy Sm30−32Fe13 Sb57−55 (HfCuSi2 type structure, a = 0.43252–0.43261, c = 0.95025–0.95156). For the sample preparation and the purity of starting materials, see LaFe1−x Sb2 . The crystal structure of the SmFe4 Sb12 compound was studied by Evers et al. (1995). It was found to adopt the LaFe4 P12 type, a = 0.9130 (X-ray powder diffraction). The purities of the materials were 99.9% or better. Filings of the samarium were prepared under argon and annealed with the corresponding amounts of antimony in evacuated sealed silica tubes for two days at 723 K, followed by ﬁve days at 1023 K. The resulting antimonide SmSb was ground together with appropriate amounts of Fe and Sb, pressed into pellets and sealed in evacuated silica tubes. The ampoules were quickly heated to 913 K, kept at this temperature for 24 h, and then quenched. The starting composition was Sm:Fe:Sb = 2:4:13. The excess antimony was removed by treating the product for several days with concentrated hydrochloric acid. From a room temperature X-ray powder diffraction analysis Sm6 Fe13 Sb was found to crystallize with the ordered La6 Co11 Ga3 , i.e., the Nd6 Fe13 Si type, a = 0.8041, c = 2.3048

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(Weitzer et al., 1993). An alloy was synthesized from ingots and compacted powders of the constituent elements 99.9% pure by arc melting followed by annealing at 1073 for 3 days and quenched in cold water. The binary Sm2 Fe17 compound dissolves about 6 at.% of Sb at 1223 K (Zhang et al., 2000). 3.1.7.6. Sm–Co–Sb. Leithe-Jasper and Rogl (1994) investigated the formation and crystal structure of the SmCo1−x Sb2 compound by X-ray powder analysis of the alloy Sm28 Co17 Sb55 (HfCuSi2 type structure, a = 0.43415, c = 0.96700). For the sample preparation and the purity of starting materials, see LaFe1−x Sb2 . Wollesen et al. (1996) conﬁrmed the crystal structure by using X-ray powder diffraction: a = 0.43346, c = 0.9650 for SmCo1−x Sb2 . For synthesis, see LaMn0.721 Sb2 . The purities of the starting elements were: Sm, greater than 99.9%, Co, greater than 99.8%, Sb 99.9%. 3.1.7.7. Sm–Ni–Sb. Pankevich et al. (1983) reported the crystal structure for the SmNiSb2 compound, HfCuSi2 type structure, a = 0.4335, c = 0.9513 (X-ray powder diffraction; arc melted and annealed at 870 K for two weeks). The crystallographic characteristics were conﬁrmed by Sologub et al. (1994), a = 0.43406, c = 0.9523. For experimental details, see LaNiSb2 . Early investigations of SmNiSb showed that it had the AlB2 type structure with a = 0.4372, c = 0.3843 (Pecharsky et al., 1983a; X-ray powder analysis). For experimental procedure, see ScNiSb. At variance with these data, Hartjes and Jeitschko (1995) suggested ZrBeSi type structure, a = 0.4387, c = 0.7699 from X-ray powder diffraction. For experimental details, see LaNiSb. CeGa2 Al2 type structure was reported for SmNi2 Sb2 by Pecharsky et al. (1982), a = 0.4261, c = 0.9838 from X-ray powder diffraction. For sample preparation, see CeNi2 Sb2 . Hoffman and Jeitschko (1988) established a defect CaBe2 Ge2 type structure for SmNi2−x Sb2 alloy, a = 0.4281, c = 0.9838, X-ray powder diffraction. Sample preparation, see CeNi2−x Sb2 . 3.1.7.8. Sm–Cu–Sb. A ternary compound of samarium with copper and antimony of the stoichiometric ratio 3:3:4 was identiﬁed and studied by means of X-ray analysis by Skolozdra et al. (1993). The compound Sm3 Cu3 Sb4 was found to have the Y3 Au3 Sb4 type structure with a lattice parameter of a = 0.9620 (X-ray powder diffraction). For experimental details, see the Y–Cu–Sb system. SmCuSb2 crystallizes with a HfCuSi2 type structure with the lattice parameters of a = 0.42939, c = 0.9999 (Sologub et al., 1994). For experimental details, see LaNiSb2 . 3.1.7.9. Sm–Zn–Sb. Sologub et al. (1995b) reported on the crystallographic data for the SmZn1−x Sb2 compound (HfCuSi2 type structure, a = 0.42997, c = 1.0272; X-ray powder diffraction) which was obtained from a multiphase alloy. For the sample preparation and the purity of starting materials, see CeZn1−x Sb2 . Wollesen et al. (1996) conﬁrmed the crystal structure of SmZn1−x Sb2 by using X-ray powder diffraction: a = 0.43010, c = 1.0271.

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For experimental details, see LaMn0.721Sb2 . The purities of the starting elements were: Sm, greater than 99.9%, Zn, greater than 99.8%, Sb 99.9%. The crystal structure of the Sm6 ZnSb15 compound was investigated by Sologub et al. (1996b) by the X-ray powder diffraction. It was found to crystallize with the La6 MnSb15 structure type, a = 1.5004, b = 1.8794, c = 0.41769. For sample preparation, see Ce6 ZnSb15. 3.1.7.10. Sm–Ga–Sb. SmGaSb2 crystallizes with the NaCl type structure, a = 0.60896 (Kuliev et al., 1990). Mills and Mar (2000) established the crystal structure for the Sm12 Ga4 Sb23 compound from X-ray powder diffraction (Pr12 Ga4 Sb23 type, a = 0.4213, b = 1.9120, c = 2.6009). The sample was synthesized by direct reaction of the elements in evacuated silica tubes. 3.1.7.11. Sm–Ge–Sb. Lam et al. (2001) investigated the crystal structure of the Sm6 Ge5−x Sb11+x compound using X-ray powder diffraction (La6 Ge2.8 Sb13.2 type structure, a = 0.41942, b = 1.0537, c = 2.6350). 3.1.7.12. Sm–Se–Sb. Rustamov et al. (1981b) reported from X-ray powder diffraction the crystal structure of the compound Sm3 Se9 Sb4 obtained by using a chemical vapour transport technique, Eu3 S9 Sb4 structure type, a = 1.744, b = 0.410, c = 2.492. 3.1.7.13. Sm–Nb–Sb. Sm3 NbSb5 crystallizes with the Hf5 CuSn3 anti-type structure, a = 0.9344, c = 0.6234 (X-ray powder diffraction; Bollore et al., 1995). 3.1.7.14. Sm–Ru–Sb. The crystal structure of the SmRu4 Sb12 compound was investigated by Evers et al. (1995). It crystallizes with the LaFe4 P12 type structure, a = 0.9259 (X-ray powder diffraction). The purities of the materials were 99.9% or better. Filings of samarium were prepared under argon and annealed with the corresponding amounts of antimony in evacuated sealed silica tubes for two days at 723 K, followed by ﬁve days at 1023 K. The resulting antimonide SmSb was ground together with appropriate amounts of Ru and Sb, pressed into pellets and sealed in evacuated silica tubes. The ampules were quickly heated to 873 K, were kept at this temperature for 24 h, and were then quenched. The starting composition was Sm:Ru:Sb = 2:4:13. The excess antimony was removed by treating the product for several days with concentrated hydrochloric acid. 3.1.7.15. Sm–Pd–Sb. Marazza et al. (1980) established the CaIn2 type structure with a = 0.4572, c = 0.7546 for the SmPdSb compound by using X-ray powder diffraction and metallographic analyses. For the sample preparation and the purity of the starting components, see Y–Pd–Sb system. The crystallographic characteristics were conﬁrmed from X-ray powder diffraction of arc-melted and annealed at 1073 K alloys: CaIn2 type, a = 0.4578, c = 0.7527 (Zygmunt and Szytula, 1995). SmPdSb2 was found to adopt the HfCuSi2 type structure with lattice parameters of a = 0.44315, c = 0.9627 (Sologub et al., 1994). For experimental details, see LaNiSb2 .

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Hoffman and Jeitschko (1988) established the CaBe2 Ge2 type structure for SmPd2 Sb2 , X-ray powder diffraction. The sample was synthesized in the same manner as LaPd2 Sb2 . 3.1.7.16. Sm–Ag–Sb. SmAgSb2 was observed and studied by Sologub et al. (1995a). It was found to crystallize with HfCuSi2 type structure with lattice parameters as follows a = 0.43126, c = 1.0548 by X-ray powder diffraction of arc melted and annealed at 870 K for 14 days alloy. The purity of the starting materials was 99.9 wt.%. The existence and crystal structure of SmAgSb2 compound were independently conﬁrmed by Brylak et al. (1995) (a = 0.4312, c = 1.0555; X-ray powder diffraction). For sample preparation, see YAgSb2 . The starting materials were: Sm 99.9%, Ag M3N, and Sb 325 mesh, M2N5. 3.1.7.17. Sm–Cd–Sb. Sologub et al. (1995b) reported on the crystallographic data for the SmCdSb2 compound (HfCuSi2 type structure, a = 0.43301, c = 1.0782; X-ray powder diffraction) which obtained from a multiphase alloy. For the sample preparation and the purity of the starting materials, see CeZn1−x Sb2 . Wollesen et al. (1996) conﬁrmed the crystal structure by using X-ray powder diffraction: a = 0.43165, c = 1.078 for SmCd1−x Sb2 . For experimental details, see LaMn0.721(1)Sb2 . The purities of the starting elements were: Sm, greater than 99.9%, Cd, greater than 99.8%, Sb 99.9%. 3.1.7.18. Sm–Sn–Sb. The NdTe3 type structure was reported for Sm2 SnSb3 , a = 0.4228, b = 2.299, c = 0.4478 from an X-ray single crystal investigation (Wang et al., 1967). The single crystal was isolated from a sample obtained by heating starting components at 773 K for 24 h, 973 K for 1 week and 1023 K for 15 days. Ferguson et al. (1996) investigated the crystal structure of the SmSnx Sb2 by using X-ray powder diffraction a = 0.4174, b = 2.2384, c = 0.4416. The sample was synthesized by direct reaction of the elements at 1223 K. 3.1.7.19. Sm–Te–Sb. The complete c–T diagrams were presented for the Sb2 Te3 –Sm2 Te3 and Sb2 Te3 –SmTe sections by Geidarova and Rustamov (1985) and Sadygov et al. (1988a), respectively. The SmTe3 Sb compound, which formed by incongruent melting, was observed by Geidarova and Rustamov (1985) to have the Bi2 Te3 structure type, a = 0.446, c = 3.020. Sadygov et al. (1988a) reported from X-ray powder diffraction the crystal structure for two compounds: SmTe4 Sb2 , Th3 P4 structure type, a = 1.049 and SmTe7 Sb4 , Th3 P4 , a = 1.072. The samples were prepared by heating in evacuated quartz tubes at 1450 K and oven cooling. SmSbTe crystallizes with the Cu2 Sb structure type, a = 0.4287, c = 0.9307 after Charvillat et al. (1977). 3.1.7.20. Sm–Hf–Sb. Bollore et al. (1995) studied the crystal structure of the Sm3 HfSb5 compound. It was found to form the Hf5 CuSn3 anti-type structure, a = 0.9340, c = 0.6230 (X-ray powder diffraction).

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3.1.7.21. Sm–Os–Sb. The SmOs4 Sb12 compound forms the LaFe4 P12 type structure, a = 0.93009 after Braun and Jeitschko (1980) (X-ray powder diffraction). The purities of the starting materials and the experimental procedure were the same as for LaFe4 Sb12 . 3.1.7.22. Sm–Pt–Sb. SmPtSb crystallizes with the MgAgAs-type structure, a = 0.6554 (Rossi et al., 1981; powder X-ray diffraction data). For the experimental details, see the LaPtSb system. 3.1.7.23. Sm–Au–Sb. The Y3 Au3 Sb4 type structure was reported by Dwight (1977) for the Sm3 Au3 Sb4 alloy (a = 0.9909; X-ray powder diffraction). The conditions of synthesis were not speciﬁed. SmAuSb2 was found to adopt the HfCuSi2 type structure with lattice parameters of a = 0.43653, c = 1.0134 (Sologub et al., 1994). For experimental details, see LaNiSb2 . 3.1.8. Eu–M–Sb systems 3.1.8.1. Eu–Li–Sb. The EuLiSb compound has the TiNiSi structure type: a = 0.7914, b = 0.4773, c = 0.8358 (Albering et al., 1997). 3.1.8.2. Eu–Mn–Sb. Rühl and Jeitschko (1979) reported the results of an X-ray powder investigation of EuMn2Sb2 which has the CaAl2 Si2 type structure, a = 0.4570, c = 0.7660. The proper amounts of the starting elements were heated in an evacuated tube at 1200–1250 K for 1 week and rapidly quenched. Eu14 MnSb11 forms the Ca14 AlSb11 type structure, a = 1.7300, c = 2.2746 (X-ray single crystal diffraction; Rehr and Kauzlarich, 1994). A single crystal was isolated from a sample obtained by heating the starting components (Eu, Mn, and Sb (6N)) in a quartz tube under argon at 1523 K for 24 hours. 3.1.8.3. Eu–Fe–Sb. The crystal structure of the EuFe4 Sb12 compound was investigated by Evers et al. (1995). It was found to adopt the LaFe4 P12 type structure, a = 0.9165 (X-ray powder diffraction). The purities of the materials were 99.9% or better. Filings of europium were prepared under argon and annealed with the corresponding amounts of antimony in evacuated sealed silica tubes for two days at 723 K, followed by ﬁve days at 1023 K. The resulting antimonide EuSb2 was ground together with the appropriate amounts of Fe and Sb, pressed into pellets and sealed in evacuated silica tubes. The ampules were quickly heated to 933 K, kept at this temperature for 3 h, cooled at 1 ◦ C/h to 873 K and then quenched. The starting composition was Eu:Fe:Sb = 2:4:14. The excess antimony was removed by treating the product for several days with concentrated hydrochloric acid. 3.1.8.4. Eu–Ni–Sb. Marchand and Jeitschko (1978) investigated the crystal structure of the EuNi2 Sb2 compound (ThCr2Si2 type structure: a = 0.43834, c = 1.0664; X-ray powder diffraction). Stoichiometric amounts of the elemental components (Eu, Ni better than 99.5%, Sb better than 99%) were sealed under argon in silica tubes, heated at 920 K for 12 h, followed by 4 h at 1250 K and rapid cooling. The samples were then ground to powder, cold pressed to

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small pellets, resealed in silica tubes under Ar, and annealed for 15 h at 1250 K. The structure reﬁnement from single crystal data conﬁrmed the structure type and established the composition as EuNi1.53Sb2 and the lattice parameters as a = 0.4340, c = 1.0597 (Hoffman and Jeitschko, 1985). A single crystal was selected from a sample prepared by annealing the elemental components for 5 days at 1073 K. The resulting button was melted in a high-frequency furnace and quenched. 3.1.8.5. Eu–Cu–Sb. EuCuSb was found to crystallize with the ZrBeSi type structure with lattice parameters of a = 0.4512, c = 0.8542 (Tomuschat and Schuster, 1981; X-ray photographic powder method). Dunner et al. (1995) reported the crystal structure for the EuCu2Sb2 compound to have the CaBe2 Ge2 type structure, a = 0.4504, c = 1.0824 (powder and single crystal diffraction). The sample was obtained by the reaction: 2Eu + 2CuCl + 2Sb → EuCu2 Sb2 + EuCl2 , and annealed at 1120 K for 100 h. 3.1.8.6. Eu–Zn–Sb. EuZn2Sb2 with the CaAl2 Si2 type structure (a = 0.4489, c = 0.7609; X-ray powder diffraction data) was obtained by Klüfers et al. (1980) from an alloy melted in a corundum crucible at 1173–1373 K for 4–6 hours and annealed at 1373–1473 K for 4–48 hours. 3.1.8.7. Eu–Se–Sb. EuSe4 Sb2 was found by Rustamov et al. (1977) to form PbS4 Bi2 structure type, a = 1.14, b = 0.376, c = 1.42 in an alloy obtained by melting the starting components in evacuated quartz tube at 1373–1423 K. The crystal structure was conﬁrmed by Aliev et al. (1978) for a sample prepared by a chemical transport reaction technique: a = 1.137, b = 0.400, c = 1.135 from single crystal X-ray diffraction. Rustamov et al. (1981b) and Aliev et al. (1986) reported the crystal structure for the Eu3 Se9 Sb4 compound, Eu3S9 Sb4 structure type, a = 1.717, b = 0.406, c = 2.488 from X-ray powder diffraction. The sample was prepared by a chemical vapour transport technique. 3.1.8.8. Eu–Ru–Sb. The crystal structure of the EuRu4 Sb12 compound was investigated by Braun and Jeitschko (1980). It was found to form the LaFe4 P12 type structure, a = 0.92824 (X-ray powder diffraction). The purities of starting materials and experimental procedure were the same as for LaRu4 Sb12 . These results were conﬁrmed by Evers et al. (1995), a = 0.9284 from an X-ray single crystal analysis. 3.1.8.9. Eu–Pd–Sb. The structure reﬁnement from single crystal data established the CaBe2 Ge2 type structure for EuPd2 Sb2 a = 0.4629, c = 1.0568 (Hoffman and Jeitschko, 1985). A single crystal was isolated from the sample prepared by annealing the elemental components for 10 days at 1020 K. The resulting button was oven cooled. EuPdSb crystallizes with the TiNiSi type structure, a = 0.7627, b = 0.4695, c = 0.7925 (Malik and Adroja, 1991c; powder X-ray diffraction data). Starting elements (Eu 4N, Pd 4N, Sb 4N) were arc melted under argon.

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3.1.8.10. Eu–Ag–Sb. EuAgSb was found to crystallize with the ZrBeSi type structure with lattice parameters of a = 0.4755, c = 0.8283 (Tomuschat and Schuster, 1981). 3.1.8.11. Eu–Sn–Sb. The ternary compound EuSn3Sb4 was synthesized at 1173 K in a tin ﬂux, and its crystal structure was determined by X-ray single crystal diffraction methods. It crystallizes in the orthorhombic Pnma space group with lattice parameters a = 0.9954, b = 0.43516, c = 2.2650 (Lam et al., 2000). 3.1.8.12. Eu–Te–Sb. Aliev and Rustamov (1978) reported the c–T diagram for the EuTe– Sb2 Te3 section. EuTe4 Sb2 belongs to a Th3 P4 structure type, a = 1.044 after Aliev et al. (1985). The same group of authors studied the crystal structure for EuTe7Sb4 , Th3 P4 structure type, a = 1.062 (Aliev et al., 1986). Hulliger and Ott (1977) reported the anti-Th3P4 structure type for Eu4 TeSb2 , a = 0.9814 from X-ray powder diffraction. The sample was placed in tantalum or molybdenum crucible and heated in quartz tube below 1273 K. 3.1.8.13. Eu–Os–Sb. The crystal structure of the EuOs4 Sb12 compound was investigated by Braun and Jeitschko (1980). It belongs to the LaFe4 P12 type structure, a = 0.93187 (X-ray powder diffraction). The purities of the starting materials and the experimental procedure were the same as for LaFe4 Sb12 . 3.1.8.14. Eu–Pt–Sb. EuPtSb was found to form the TiNiSi type structure (a = 0.7581, b = 0.4642, c = 0.7893) from X-ray single crystal diffraction by Wenski and Mewis (1986b). 3.1.8.15. Eu–Au–Sb. Tomuschat and Schuster (1981) reported the ZrBeSi type structure for EuAuSb, a = 0.4669, c = 0.8486 (X-ray photographic powder method). The sample was synthesized by melting the starting components in corundum crucible under argon at 1273 K 12–16 h and annealing at 1373 K 14 h. Suzuki et al. (1993) established a CaIn2 type structure for EuAuSb, a = 0.4681, c = 0.8422. For the sample preparation, see CeAuSb. 3.1.9. Gd–M–Sb systems 3.1.9.1. Gd–Li–Sb. A systematic study of the Gd–Li–Sb system at 470 K was performed by Pavlyuk (1993) over the whole concentration region by means of X-ray powder analysis (ﬁg. 19). The samples were prepared by arc melting under argon and annealed in evacuated quartz ampoules at 470 K for 10 days. Five ternary phases were observed, the crystal structure was established only for two of them: GdLi3 Sb2 (2), YLi3 Sb2 type structure, a = 0.4547, c = 0.7196 (powder diffraction) and Gd3 Li4 Sb4 (3), Gd6 Cu8 Ge8 type structure, a = 1.4594, b = 0.4513, c = 0.7100 (powder diffraction). Crystal structure for last three compounds ∼GdLi7 Sb2 (1), ∼Gd4 Li3 Sb4 (4) and ∼Gd2 LiSb (5) have not been investigated. No homogeneous ranges were encountered for the ternary compounds. The liquid immiscibility region, existing in the Gd–Li binary system, extends to 20 at.% Ge in the ternary system.

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Fig. 19. Gd–Li–Sb, isothermal section at 470 K.

3.1.9.2. Gd–Cr–Sb. Ferguson et al. (1997) investigated the crystal structure of the GdCrSb3 compound (CeCrSb3 type structure: a = 1.2760, b = 0.6153, c = 0.6004, X-ray powder diffraction). 3.1.9.3. Gd–Fe–Sb. Leithe-Jasper and Rogl (1994) investigated the formation and crystal structure of the GdFe1−x Sb2 compound by X-ray powder analysis of the alloy Gd35Fe10 Sb55 (HfCuSi2 type structure, a = 0.43080, c = 0.94125). For the sample preparation and the purity of the starting materials, see LaFe1−x Sb2 . 3.1.9.4. Gd–Ni–Sb. GdNiSb2 is isostructural with the HfCuSi2 type structure with lattice parameters of a = 0.43345, c = 0.9452 (Sologub et al., 1994). The alloy was prepared in the same manner as YCuSb2 . Early investigations of the GdNiSb compound showed that it had the MgAgAs-type with a = 0.6340 (Dwight, 1974) from X-ray powder analysis of an alloy arc melted under argon and annealed at 973 K. Hartjes and Jeitschko (1995) conﬁrmed the crystal structure and obtained the lattice parameter of a = 0.6323 by X-ray powder diffraction. For experimental details, see LaNiSb. At variance to these data, Pecharsky et al. (1983a) suggested the AlB2 type structure with a = 0.4329, c = 0.3918 from X-ray powder analysis of an alloy arc melted under argon and annealed at 870 K. Marchand and Jeitschko (1978) investigated the crystal structure of GdNi2 Sb2 compound (ThCr2 Si2 type structure: a = 0.4259, c = 0.9809; X-ray powder diffraction). For the sample preparation, see EuNi2 Sb2 . A later investigation (Hoffman and Jeitschko, 1988) established the defect CaBe2 Ge2 type structure for the GdNi2−x Sb2 alloy, a = 0.4261, c = 0.9741, X-ray powder diffraction. For the experimental details, see CeNi2−x Sb2 . The same authors investigated the antimony rich section of the ternary system Gd–Ni–Sb at 1070 K. Except for GdNi2−x Sb2 , no other ternary compound with a high antimony content was observed. In sam-

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ples quenched from 1070 K GdNi2−x Sb2 was found to be in equilibrium with GdSb, elemental antimony, NiSb and the high temperature modiﬁcation of Ni3 Sb. Kaczmarska et al. (1995) conﬁrmed the crystal structure with similar lattice parameters for GdNi2 Sb2 ; CaBe2 Ge2 type structure, a = 0.4288, c = 0.9763 from powder diffraction of arc melted alloys. Mozharivskyj and Franzen (2000b) reported the crystal structure of the Gd5 Ni2 Sb (Mo5 B2 Si structure type, a = 0.7698, c = 1.3403) from X-ray powder diffraction of arc melted and annealed at 1070 K for 10 days alloy. 3.1.9.5. Gd–Cu–Sb. A ternary compound of gadolinium with copper and antimony of the 3:3:4 stoichiometric ratio was identiﬁed and studied by means of X-ray analysis by Skolozdra et al. (1993). Gd3 Cu3 Sb4 compound was found to have the Y3 Au3 Sb4 type with the lattice parameter of a = 0.9571 (X-ray powder diffraction). For experimental details, see the Y–Cu– Sb system. At variance with these data, Patil et al. (1996) reported a tetragonal distortion of the cubic crystal structure Y3 Cu3 Sb4 for the Gd3 Cu3 Sb4 alloy which was prepared by arc melting the constituent elements of purity better than 99.9% in an argon atmosphere and annealed at 1070 K for one week (a = 0.958, c = 0.972; X-ray powder diffraction). GdCuSb2 was found to form the HfCuSi2 type structure with lattice parameters of a = 0.42783, c = 0.9946 (Sologub et al., 1994). For experimental details, see LaNiSb2 . Kaczmarska et al. (1995) established the crystal structure for the GdCu2 Sb2 compound; CaBe2 Ge2 type structure, a = 0.4266, c = 0.9953 from powder diffraction of arc melted alloys. 3.1.9.6. Gd–Zn–Sb. Sologub et al. (1995b) reported on the crystallographic data for the GdZn1−x Sb2 compound (HfCuSi2 type structure, a = 0.42838, c = 1.0242; X-ray powder diffraction) which was obtained from a multiphase alloy. For the sample preparation and the purity of the starting materials, see CeZn1−x Sb2 . Wollesen et al. (1996) conﬁrmed the crystal structure by using X-ray powder diffraction: a = 0.42748, c = 1.02614 for GdZn1−x Sb2 . For experimental details, see LaMn0.721(1)Sb2 . The purities of the starting elements were: Gd, greater than 99.9%, Zn, greater than 99.8%, Sb 99.9%. The crystal structure of the Gd6 ZnSb15 compound was investigated by Sologub et al. (1996a) by the X-ray powder diffraction. It was found to crystallize with the La6 MnSb15 structure type, a = 1.4942, b = 1.8740, c = 0.41528. For the sample preparation, see Ce6 ZnSb15. 3.1.9.7. Gd–Ge–Sb. Lam et al. (2001) determined the crystal structure of the Gd6 Ge4.3 Sb11.7 compound, a = 0.41509, b = 1.04438, c = 2.6240 from X-ray single crystal diffraction data. The sample was synthesized by direct reaction of the elements at 1223 K. 3.1.9.8. Gd–Se–Sb. Aliev et al. (1977) constructed the complete c–T diagram for the Gd2 Se3 –Sb2 Se3 section. The GdSe30 Sb19 compound with the S3 Sb2 type structure, a = 1.173, b = 0.412, c = 1.1846 was observed from a sample annealed at 723–773 K for 300 h. A small homogeneity ﬁeld was found for (Gdx Sb1−x )2 Se3 : x = 0–0.05, a = 1.162–1.173, b = 0.396–0.412, c = 1.177–1.1846.

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3.1.9.9. Gd–Zr–Sb. Morozkin and Sviridov (2001) investigated the crystal structure of the GdZrSb compound by X-ray powder diffraction. The CeScSi structure type was established, a = 0.4261, c = 1.6455. 3.1.9.10. Gd–Pd–Sb. Marazza et al. (1980) established the CaIn2 type structure with a = 0.4566, c = 0.7452 for the GdPdSb compound by using X-ray powder diffraction and metallographic analyses. For the sample preparation and the purity of the starting components, see Y–Pd–Sb system. Malik and Adroja (1991a) conﬁrmed the crystal structure and lattice parameters, a = 0.4565, c = 0.7443 (X-ray diffraction; arc melted alloy). GdPdSb2 was found to adopt a HfCuSi2 type structure with lattice parameters of a = 0.44150, c = 0.9567 (Sologub et al., 1994). For experimental details, see LaNiSb2 . Mozharivskyj and Franzen (2000b) established the crystal structure of Gd5 Pd2 Sb to be isotypic with Mo5 B2 Si type structure, a = 0.7812, c = 1.3645 from the X-ray powder diffraction of arc melted and annealed at 1070 K for 10 days alloy. 3.1.9.11. Gd–Ag–Sb. GdAgSb2 compound was observed and studied by Sologub et al. (1995a). It was found to crystallize with HfCuSi2 type structure with lattice parameters of a = 0.42965, c = 1.0518 by X-ray powder diffraction of arc melted and annealed at 870 K for 14 days alloy. The purity of the starting materials was 99.9 wt.%. The existence and crystal structure of GdAgSb2 compound were independently conﬁrmed by Brylak et al. (1995) (a = 0.42952, c = 1.0506; X-ray powder diffraction). For the sample preparation, see YAgSb2 . The purity of the starting materials was: Gd 99.9%, Ag M3N, and Sb 325 mesh, M2N5. 3.1.9.12. Gd–Te–Sb. The complete c–T diagram was presented for the GdTe–Sb2 Te3 section by Rustamov and Geidarova (1984). Charvillat et al. (1977) determined the Cu2 Sb structure type for the GdSbTe compound, a = 0.4262, c = 0.9258 from a GdSb0.97Te alloy and observed the existence of a homogeneity ﬁeld: GdTex Sb, x = 0.86–0.97, a = 0.4274–0.4262, c = 0.9243–0.9258. 3.1.9.13. Gd–Pt–Sb. The X-ray powder analysis of the GdPtSb compound showed that it had the MgAgAs type structure with a = 0.6585 (Dwight, 1974). For the sample preparation, see ScNiSb. Mozharivskyj and Franzen (2001) reported the crystal structure for the Gd5 Pt2 Sb compound from X-ray powder diffraction data: Mo5 B2 Si type structure, which is an ordered version of the Cr5 B3 structure type, a = 0.7801, c = 1.3556. For the experimental procedure, see Y5 Pt2 Sb. 3.1.9.14. Gd–Au–Sb system. The Y3 Au3 Sb4 type structure was reported by Dwight (1977) for the Gd3 Au3 Sb4 alloy (a = 0.9864; X-ray powder diffraction). The conditions of synthesis were not speciﬁed.

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O.L. SOLOGUB AND P.S. SALAMAKHA Table 2 Lattice parameters of the Gd4 (Bix Sb1−x )3 alloys Bi concentration, x 0 0.25 0.50 0.75 1.00

a 0.92328 0.92680 0.93072 0.93449 0.93906

3.1.9.15. Gd–Bi–Sb. Niu et al. (2001) reported on the lattice parameters for the Gd4 (Bix Sb1−x )3 series with x = 0, 0.25, 0.5, 0.75 and 1 (table 2). 3.1.10. Tb–M–Sb 3.1.10.1. Tb–Li–Sb. One ternary compound, TbLi2Sb2 , was observed with an unknown crystal structure (Pavlyuk, 1993). 3.1.10.2. Tb–Cr–Sb. Ferguson et al. (1997) established the crystal structure of the TbCrSb3 compound: CeCrSb3 type structure, a = 1.2680, b = 0.6143, c = 0.6003 from X-ray powder diffraction. 3.1.10.3. Tb–Ni–Sb. Mozharivskyj and Kuz’ma (1996) investigated the crystal structure of Tb5 Ni2 Sb (Mo5B2 Si type structure, a = 0.7641, c = 1.3266; X-ray powder diffraction). The alloy was prepared in the same manner as Y5 Ni2 Sb. The starting materials were Tb not less than 99.8 wt.%, Ni and Sb 99.9 mass%. TbNiSb2 was found to crystallize with the HfCuSi2 type structure with lattice parameters of a = 0.43201, c = 0.9361 (Sologub et al., 1994). The alloy was prepared in the same manner as YCuSb2 . An early investigation of the TbNiSb compound showed that it had the MgAgAs-type with a = 0.6327 (Dwight, 1974), from an X-ray powder analysis of an alloy arc melted under argon and annealed at 973 K. Pecharsky et al. (1983a) and Hartjes and Jeitschko (1995) conﬁrmed the crystal structure and obtained the lattice parameters as a = 0.6302 and a = 0.6304, respectively, by X-ray powder diffraction. For experimental details, see ScNiSb and LaNiSb respectively. Hoffman and Jeitschko (1988) established the defect CaBe2 Ge2 type structure for TbNi2−xSb2 , a = 0.42496, c = 0.9649, X-ray powder diffraction. For the sample preparation, see CeNi2−x Sb2 . 3.1.10.4. Tb–Cu–Sb. A ternary compound of terbium with copper and antimony of the 3:3:4 stoichiometric ratio was identiﬁed and studied by means of X-ray analysis by Skolozdra et al. (1993). Tb3 Cu3 Sb4 was found to have the Y3 Au3 Sb4 type structure with a lattice parameter of a = 0.9522 (X-ray powder diffraction). For experimental details, see the Y–Cu–Sb system. TbCuSb2 was found to adopt the HfCuSi2 type structure with lattice parameters of a = 0.42683, c = 0.9877 (Sologub et al., 1994). The alloy was prepared in the same manner as YCuSb2 .

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3.1.10.5. Tb–Zn–Sb. Wollesen et al. (1996) reported on the crystallographic data for the TbZn1−x Sb2 compound (HfCuSi2 type structure, a = 0.42611, c = 1.02297; X-ray powder diffraction). For experimental details, see LaMn0.721(1)Sb2 . The purities of the starting elements were: Tb, greater than 99.9%, Zn, greater than 99.8%, Sb 99.9%. 3.1.10.6. Tb–Ge–Sb. Lam et al. (2001) investigated the crystal structure of the Tb6 Ge5−x Sb11+x compound using X-ray powder diffraction: a = 0.41305, b = 1.0393, c = 2.6139. 3.1.10.7. Tb–Zr–Sb. Morozkin and Sviridov (2001) reported the crystal structure for the TbZrSb compound from X-ray powder diffraction data: CeScSi type structure, a = 0.4251, c = 1.6380. 3.1.10.8. Tb–Pd–Sb. Marazza et al. (1980) established the CaIn2 type structure with a = 0.4550, c = 0.7384 for the TbPdSb compound by using X-ray powder diffraction and metallographic analyses. For the sample preparation and the purity of the starting components, see Y–Pd–Sb system. The crystallographic characteristics were conﬁrmed from powder diffraction data of arc melted and annealed at 1073 K alloys: CaIn2 type structure, a = 0.4551, c = 0.7411 (Zygmunt and Szytula, 1995). TbPdSb2 was found to adopt the HfCuSi2 type structure with lattice parameters of a = 0.44097, c = 0.9480 (Sologub et al., 1994). For experimental details, see LaNiSb2 . Mozharivskyj and Franzen (2000b) investigated the crystal structure of Tb5 Pd2 Sb, which has the Mo5 B2 Si structure type, a = 0.7730, c = 1.3508 by X-ray powder diffraction of arc melted and annealed at 1070 K for 10 days alloy. 3.1.10.9. Tb–Ag–Sb. TbAgSb2 compound was observed and studied by Sologub et al. (1995a). It was found to crystallize with HfCuSi2 type structure with lattice parameters as follows: a = 0.42774, c = 1.0477 by X-ray powder diffraction of arc an melted and annealed at 870 K for 14 days alloy. The purity of starting materials was 99.9 wt.%. The existence and crystal structure of the TbAgSb2 compound were independently conﬁrmed by Brylak et al. (1995) (a = 0.42833, c = 1.0476; X-ray powder diffraction). For the sample preparation, see YAgSb2 . The starting materials were: Tb 99.9%, Ag M3N, and Sb 325 mesh, M2N5. 3.1.10.10. Tb–Te–Sb. Rustamov and Geidarova (1984) constructed the complete c–T diagram for the TbTe–Sb2Te3 section. 3.1.10.11. Tb–Pt–Sb. An investigation of the TbPtSb compound by X-ray powder diffraction showed that it had the MgAgAs type structure with a = 0.6540 (Dwight, 1974). For the sample preparation, see ScNiSb. Mozharivskyj and Franzen (2001) reported the crystal structure for the Tb5 Pt2 Sb compound from X-ray powder diffraction data: Mo5 B2 Si type structure, which is an ordered version of the Cr5 B3 structure type, a = 0.7748, c = 1.3463. For the experimental procedure, see Y5 Pt2 Sb.

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3.1.10.12. Tb–Au–Sb. The Tb3 Au3 Sb4 alloy was reported by Dwight (1974) to have the Y3 Au3 Sb4 type structure (a = 0.9834; X-ray powder diffraction). The conditions of synthesis were not speciﬁed. The same structure type was conﬁrmed by Shaked et al. (1979) for a Tb3 Au3 Sb4 sample obtained by arc melting the correct amounts of the elemental materials in a helium/argon atmosphere. The alloy was annealed at 960 K for one week and water quenched. 3.1.11. Dy–M–Sb systems 3.1.11.1. Dy–Cr–Sb. Ferguson et al. (1997) investigated the crystal structure of the DyCrSb3 compound, CeCrSb3 type structure: a = 1.229, b = 0.6135, c = 0.5978 by X-ray powder diffraction. 3.1.11.2. Dy–Ni–Sb. Mozharivskyj and Kuz’ma (1996) investigated the crystal structure of Dy5 Ni2 Sb (Mo5 B2 Si type structure, a = 0.7593, c = 1.3258; X-ray powder diffraction). The alloy was prepared in the same manner as Y5 Ni2 Sb. The starting materials were: Dy not less than 99.8 wt.%, Ni and Sb 99.9 wt.%. DyNiSb2 was found to adopt the HfCuSi2 type structure with the lattice parameters of a = 0.43029, c = 0.9305 (Sologub et al., 1994). For experimental details, see LaNiSb2 . Dwight (1974) investigated the solubility of Ni in DySb: (DySb)1−x Nix , x = 0–0.26, NaCl type structure, a = 0.6155–0.6255. The same author established from X-ray powder analysis the crystal structure of DyNiSb: MgAgAs-type, a = 0.6308 (Dwight, 1974). For the sample preparation, see ScNiSb. Pecharsky et al. (1983a) and Hartjes and Jeitschko (1995) conﬁrmed the crystal structure and obtained lattice parameters of a = 0.6279 and a = 0.6298, respectively, by X-ray powder diffraction. For experimental details, see ScNiSb and LaNiSb, respectively. Hoffman and Jeitschko (1988) established the defect CaBe2 Ge2 type structure for DyNi2−x Sb2 alloy, a = 0.4207, c = 0.9587, X-ray powder diffraction. For the sample preparation, see CeNi2−x Sb2 . 3.1.11.3. Dy–Cu–Sb. A ternary compound of dysprosium with copper and antimony of the 3:3:4 stoichiometric ratio was identiﬁed and studied by means of X-ray analysis by Skolozdra et al. (1993). Dy3 Cu3 Sb4 compound was found to have the Y3 Au3 Sb4 type structure with a lattice parameter of a = 0.9503 (X-ray powder diffraction). For experimental details, see the Y–Cu–Sb system. DyCuSb2 was found to form the HfCuSi2 type structure with lattice parameters of a = 0.42669, c = 0.9817 (Sologub et al., 1994). For the experimental details, see LaNiSb2 . 3.1.11.4. Dy–Ge–Sb. Lam et al. (2001) investigated the crystal structure of the Dy6 Ge5−x Sb11+x compound by using an X-ray powder diffraction method: La6 Ge2.8 Sb13.2 type structure, a = 0.41032, b = 1.0345, c = 2.6041. 3.1.11.5. Dy–Zr–Sb. Morozkin and Sviridov (2001) determined the crystal structure of the DyZrSb compound from X-ray powder diffraction data, CeScSi type structure, a = 0.4240,

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c = 1.6349. Later Morozkin et al. (2002) from phase diagram investigation at 1070 K established that this compound has a homogeneity ﬁeld: Dy33−28Zr33−38 Sb33 . 3.1.11.6. Dy–Pd–Sb. Marazza et al. (1980) established the MgAgAs type structure with a = 0.6533 for the DyPdSb compound using X-ray powder diffraction and metallographic analyses. For the sample preparation and the purity of the starting components, see Y–Pd–Sb system. At variance with these data, Zygmunt and Szytula (1995) reported the CaIn2 type structure for this compound, a = 0.4543, c = 0.7352 from powder diffraction of arc melted and annealed at 1073 K alloys. Malik and Adroja (1991c) also observed CaIn2 type structure, a = 0.4526, c = 0.7325 for DyPdSb (powder X-ray diffraction data). Their sample also contained the MgAgAs phase. For the experimental details, see EuPdSb. DyPd2 Sb was reported to be isotypic with the crystal structure of MnCu2 Al with a lattice parameter of a = 0.6682 (Riani et al., 1995) from powder diffraction of the induction melted alloy. Mozharivskyj and Franzen (2000b) investigated the crystal structure of the Dy5 Pd2 Sb compound from an arc melted and annealed at 1070 K for 10 days alloy by using X-ray powder diffraction. The Mo5 B2 Si type structure was established, a = 0.7715, c = 1.3507. 3.1.11.7. Dy–Ag–Sb. DyAgSb2 compound was observed and studied by Sologub et al. (1995a) It was found to crystallize with the HfCuSi2 type structure with lattice parameters as follows a = 0.42733, c = 1.0453 by X-ray powder diffraction of an arc melted and annealed at 870 K for 14 days alloy. The purity of starting materials was 99.9 wt.%. The existence and crystal structure of DyAgSb2 were independently conﬁrmed by Brylak et al. (1995) (a = 0.42743, c = 1.0442; X-ray powder diffraction). For the sample preparation, see YAgSb2 . The starting materials were: Dy 99.9%, Ag M3N, and Sb 325 mesh, M2N5. 3.1.11.8. Dy–Te–Sb. The complete c–T diagrams were presented for the Sb2 Te3 –Dy2 Te3 section by Geidarova and Rustamov (1985) and by Geydarova et al. (1985), respectively. The DyTe3 Sb compound formed by incongruent melting and has the Bi2 Te3 structure type, a = 0.446, c = 3.020 (Geidarova and Rustamov, 1985). 3.1.11.9. Dy–Pt–Sb. An investigation of DyPtSb showed that it had the MgAgAs-type with a = 0.6531 (Dwight, 1974) from X-ray powder analysis. For the sample preparation, see ScNiSb. Mozharivskyj and Franzen (2001) reported the crystal structure for the Dy5 Pt2 Sb compound from X-ray powder diffraction: Mo5 B2 Si type structure, which is an ordered version of the Cr5 B3 structure type, a = 0.7686, c = 1.3420. For the experimental procedure, see Y5 Pt2 Sb. 3.1.11.10. Dy–Au–Sb. The Y3 Au3 Sb4 type structure was reported by Dwight (1977) for the Dy3 Au3 Sb4 alloy (a = 0.9811; X-ray powder diffraction). The conditions of synthesis were not speciﬁed.

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Fig. 20. Ho–Ni–Sb, isothermal sections at 770 K (0–50 at.% Sb) and 1070 K (50– 100 at.% Sb).

3.1.12. Ho–M–Sb systems 3.1.12.1. Ho–Ni–Sb. Information on the phase equilibria in the ternary Ho–Ni–Sb system is due to the work of Mozharivskyj et al. (1997) (ﬁg. 20) who employed X-ray powder diffraction on samples prepared by arc melting of the pure components. The resulting alloys were annealed at 770 K (0–50 at.% Sb) and 1070 K (50–100 at.% Sb) for 300 hours. The isothermal sections are shown in ﬁg. 20. Six ternary compounds were observed. Mozharivskyj and Kuz’ma (1996) investigated the crystal structure for Ho5 Ni2 Sb (6) (Mo5 B2 Si type structure, a = 0.7563, c = 1.3250; X-ray powder diffraction). The alloy was prepared in the same manner as Y5 Ni2 Sb. The starting materials were: Ho not less than 99.8 wt.%, Ni and Sb 99.9 wt.%. HoNiSb2 (1) was found to adopt the HfCuSi2 type structure with lattice parameters of a = 0.42989, c = 0.9257 (Sologub et al., 1994). The alloy was prepared in the same manner as YCuSb2 . An early investigation of the HoNiSb (3) compound showed that it had the MgAgAs-type with a = 0.6290 (Dwight, 1974) from an X-ray powder analysis. For the sample preparation, see ScNiSb. Pecharsky et al. (1983a) and Hartjes and Jeitschko (1995) conﬁrmed the crystal structure and obtained the same lattice parameter of a = 0.6262 by X-ray powder diffraction. For experimental details, see ScNiSb and LaNiSb, respectively. Hoffman and Jeitschko (1988) established the defect CaBe2 Ge2 type structure for the HoNi2−x Sb2 (2) alloy, a = 0.4202, c = 0.9564, X-ray powder diffraction. For the sample preparation, see CeNi2−x Sb2 . 3.1.12.2. Ho–Cu–Sb. A ternary compound of holmium with copper and antimony of the 3:3:4 stoichiometric ratio was identiﬁed and studied by means of an X-ray analysis by Skoloz-

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dra et al. (1993). Ho3 Cu3 Sb4 compound was found to have the Y3 Au3 Sb4 type structure with the lattice parameter of a = 0.9482 (X-ray powder diffraction). For experimental details, see the Y–Cu–Sb system. HoCuSb2 was found to form the HfCuSi2 type structure with lattice parameters of a = 0.42529, c = 0.9811 (Sologub et al., 1994). For experimental details, see LaNiSb2 . 3.1.12.3. Ho–Zr–Sb. Morozkin and Sviridov (2001) established the CeScSi structure type, a = 0.4201, c = 1.6143, for the HoZrSb compound from X-ray powder diffraction data. 3.1.12.4. Ho–Pd–Sb. Mozharivskyj and Kuz’ma (1996) investigated the crystal structure for Ho5 Pd2 Sb (Mo5 B2 Si type, a = 0.76795, c = 1.3476; X-ray powder diffraction). The alloy was prepared in the same manner as Y5 Ni2 Sb. The starting materials were: Ho not less than 99.8 wt.%, Pd and Sb 99.9 wt.%. Marazza et al. (1980) established the MgAgAs type structure with a = 0.6509 for the HoPdSb compound by using X-ray powder diffraction and metallographic analyses. For the sample preparation and the purity of the starting components, see Y–Pd–Sb system. The crystallographic characteristics were conﬁrmed from powder diffraction of arc melted and annealed at 1073 K alloys: MgAgAs type, a = 0.6495 (Zygmunt and Szytula, 1995). HoPd2 Sb was reported to be isotypic with the crystal structure of MnCu2 Al with a lattice parameter of a = 0.6677 (Riani et al., 1995) from powder diffraction of an induction melted alloy. 3.1.12.5. Ho–Ag–Sb. HoAgSb2 was observed and studied by Sologub et al. (1995a). It was found to crystallize with HfCuSi2 type structure with lattice parameters as follows a = 0.42665, c = 1.0427 by X-ray powder diffraction of an arc melted and annealed at 870 K for 14 days alloy. The purity of the starting materials was 99.9 wt.%. The existence and crystal structure of HoAgSb2 compound were independently conﬁrmed by Brylak et al. (1995) (a = 0.42662, c = 1.0422; X-ray powder diffraction). For sample preparation, see YAgSb2 . The starting materials were: Ho 99.9%, Ag M3N, and Sb 325 mesh, M2N5. 3.1.12.6. Ho–Pt–Sb. An X-ray powder diffraction analysis of the HoPtSb compound showed that it had the MgAgAs type structure with a = 0.6508 (Dwight, 1974). For the sample preparation, see ScNiSb. Mozharivskyj and Franzen (2001) reported the crystal structure for the Ho5 Pt2 Sb compound from X-ray powder diffraction data: Mo5 B2 Si type structure, which is an ordered version of the Cr5 B3 structure type, a = 0.7681, c = 1.3365. For the experimental procedure, see Y5 Pt2 Sb. 3.1.12.7. Ho–Au–Sb. The Ho3 Au3 Sb4 alloy was reported by Dwight (1977) to have the Y3 Au3 Sb4 type structure (a = 0.788; X-ray powder diffraction). The conditions of synthesis were not speciﬁed. These results were conﬁrmed by Shaked et al. (1979) for a Ho3 Au3 Sb4 sample obtained by arc melting the appropriate amounts of the elemental materials in a helium/argon atmosphere. The alloy was annealed at 960 K for one week and water quenched.

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3.1.13. Er–M–Sb systems 3.1.13.1. Er–Ni–Sb. Mozharivskyj and Kuz’ma (1996) investigated the crystal structure of Er5 Ni2 Sb (Mo5 B2 Si type structure, a = 0.7531, c = 1.3178; X-ray powder diffraction). The alloy was prepared in the same manner as Y5 Ni2 Sb. The starting materials were: Er not less than 99.8 wt.%, Ni and Sb 99.9 wt.%. Dwight (1974) investigated the solubility of Ni in ErSb: (ErSb)1−x Nix , x = 0–0.27, NaCl type structure, a = 0.6105–0.6220. The same author established from an X-ray powder analysis the crystal structure of ErNiSb: MgAgAs-type, a = 0.6271 (Dwight, 1974). For the sample preparation, see ScNiSb. Pecharsky et al. (1983a) and Hartjes and Jeitschko (1995) conﬁrmed the crystal structure and obtained lattice parameters of a = 0.6229 and a = 0.6247, respectively, by X-ray powder diffraction. For experimental details, see ScNiSb and LaNiSb respectively. Hoffman and Jeitschko (1988) established a defect CaBe2 Ge2 type structure for ErNi2−x Sb2 , a = 0.4194, c = 0.9608, X-ray powder diffraction. For the sample preparation, see CeNi2−x Sb2 . 3.1.13.2. Er–Cu–Sb. ErCuSb2 was found to crystallize with the HfCuSi2 type structure and lattice parameters of a = 0.42433, c = 0.9788 (Sologub et al., 1994). The alloy was prepared in the same manner as YCuSb2 . A ternary compound of erbium with copper and antimony of the 3:3:4 stoichiometric ratio was identiﬁed and studied by means of an X-ray analysis by Skolozdra et al. (1993). The Er3 Cu3 Sb4 compound was found to have the Y3 Au3 Sb4 type structure with a lattice parameter of a = 0.9458 (X-ray powder diffraction). For experimental details, see the Y–Cu–Sb system. 3.1.13.3. Er–Zr–Sb. Morozkin and Sviridov (2001) investigated the crystal structure of the ErZrSb compound by using an X-ray powder diffraction method: CeScSi structure type, a = 0.4204, c = 1.6159. 3.1.13.4. Er–Pd–Sb. Marazza et al. (1980) established the MgAgAs type structure with a = 0.6467 for the ErPdSb compound by using X-ray powder diffraction and metallographic analyses. For the sample preparation and the purity of the starting components, see Y–Pd–Sb system. ErPd2 Sb was reported to be isotypic with the crystal structure of MnCu2 Al with a lattice parameter a = 0.6667 (Riani et al., 1995) from X-ray powder diffraction of an induction melted alloy. Mozharivskyj and Franzen (2000b) investigated the crystal structure of the Er5 Pd2 Sb compound from arc melted and annealed at 1070 K for 10 days alloy by using X-ray powder diffraction. The Mo5 B2 Si structure type was established for this compound, a = 0.7641, c = 1.3465. 3.1.13.5. Er–Ag–Sb. ErAgSb2 was observed and studied by Sologub et al. (1995a). It was found to crystallize with the HfCuSi2 type structure with lattice parameters as follows a = 0.42541, c = 1.0413 by X-ray powder diffraction of an arc melted and annealed at 1070 K for

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14 days alloy. The purity of the starting materials was 99.9 wt.%. The existence and crystal structure of the ErAgSb2 compound were independently conﬁrmed by Brylak et al. (1995) (a = 0.42565, c = 1.03900; X-ray powder diffraction). For sample preparation, see YAgSb2 . The starting materials were: Er 99.9%, Ag M3N, and Sb 325 mesh, M2N5. 3.1.13.6. Er–Pt–Sb. An investigation of ErPtSb showed that it had the MgAgAs type structure with a = 0.6498 (Dwight, 1974) from an X-ray powder analysis. For the sample preparation, see ScNiSb. Mozharivskyj and Franzen (2001) reported the crystal structure of the Er5 Pt2 Sb compound from X-ray powder diffraction data: Mo5 B2 Si type structure, which is an ordered version of Cr5 B3 structure type, a = 0.7666, c = 1.3391. For the experimental procedure, see Y5 Pt2 Sb. 3.1.13.7. Er–Au–Sb. The Y3 Au3 Sb4 type structure was reported by Dwight (1977) for the Er3 Au3 Sb4 alloy (a = 0.9768; X-ray powder diffraction). The conditions of synthesis were not speciﬁed. The same structure type was conﬁrmed by Shaked et al. (1979) for an Er3 Au3 Sb4 sample obtained by arc melting the appropriate amounts of the elemental materials in a helium/argon atmosphere. The alloy was annealed at 960 K for one week and water quenched. 3.1.14. Tm–M–Sb systems 3.1.14.1. Tm–Ni–Sb. An early investigation of the TmNiSb compound showed that it had the MgAgAs type structure with a = 0.6241 (Dwight, 1974) from X-ray powder analysis. For the sample preparation, see ScNiSb. Pecharsky et al. (1983a) and Hartjes and Jeitschko (1995) conﬁrmed the crystal structure and obtained lattice parameters of a = 0.6225 and a = 0.6237, respectively, by X-ray powder diffraction. For the experimental details, see ScNiSb and LaNiSb, respectively. Mozharivskyj and Franzen (2000b) investigated the crystal structure of the Tm5 Ni2 Sb compound of an melted and annealed at 1070 K for 10 days alloy by using X-ray powder diffraction. The Mo5 B2 Si structure type was established, a = 0.7459, c = 1.325. 3.1.14.2. Tm–Cu–Sb. TmCuSb2 was found to form the HfCuSi2 type structure with the lattice parameters of a = 0.42437, c = 0.9742 (Sologub et al., 1994). For experimental details, see LaNiSb2 . 3.1.14.3. Tm–Zr–Sb. Morozkin and Sviridov (2001) established the CeScSi structure type with a = 0.4174, c = 1.5997 for the TmZrSb compound from X-ray powder diffraction data. 3.1.14.4. Tm–Pd–Sb. TmPdSb crystallizes with the MgAgAs-type structure, a = 0.6454 (Malik and Adroja, 1991c; powder X-ray diffraction data). For the experimental details, see EuPdSb. A Mo5 B2 Si structure type was established by Mozharivskyj and Franzen (2000b) for the Tm5 Pd2 Sb compound, a = 0.7585, c = 1.3457 (X-ray powder diffraction of an arc melted and annealed at 1070 K for 10 days alloy).

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3.1.14.5. Tm–Ag–Sb. TmAgSb2 was observed and studied by Sologub et al. (1995a). It was found to crystallize with the HfCuSi2 type structure with lattice parameters as follows a = 0.42481, c = 1.0395, by X-ray powder diffraction of an arc melted and annealed at 870 K for 14 days alloy. The purity of the starting materials was 99.9 wt.%. The existence and crystal structure of TmAgSb2 were independently conﬁrmed by Brylak et al. (1995) (a = 0.42529, c = 1.0390; X-ray powder diffraction). For the sample preparation, see YAgSb2 . The starting materials were: Tm 99.9%, Ag M3N, and Sb 325 mesh, M2N5. 3.1.14.6. Tm–Pt–Sb. TmPtSb forms the MgAgAs-type with a = 0.6483, Dwight (1974) from an X-ray powder analysis. For the sample preparation, see ScNiSb. Mozharivskyj and Franzen (2001) reported the crystal structure of the Tm5 Pt2 Sb compound from X-ray powder diffraction data: Mo5 B2 Si type structure, which is an ordered version of the Cr5 B3 structure type, a = 0.7584, c = 1.3394. For the experimental procedure, see Y5 Pt2 Sb. 3.1.14.7. Tm–Au–Sb. The Y3 Au3 Sb4 type structure was reported by Dwight (1977) for the Tm3 Au3 Sb4 alloy (a = 0.9752; X-ray powder diffraction). The conditions of synthesis were not speciﬁed. The same structure type was conﬁrmed by Shaked et al. (1979) for a Tm3 Au3 Sb4 sample obtained by arc melting the stoichiometric amounts of the elemental materials in a helium/argon atmosphere. The alloy was annealed at 960 K for one week and water quenched. 3.1.15. Yb–M–Sb systems 3.1.15.1. Yb–Li–Sb. YbLiSb belongs to the TiNiSi structure type with the lattice parameters of a = 0.7553, b = 0.4643, c = 0.8200 (Albering et al., 1997). 3.1.15.2. Yb–Al–Sb. Fisher et al. (2000) reported the crystal structure of the Zintl compound Yb14 AlSb11 , to have the Ca14 AlSb11 structure type, a = 1.6561, c = 2.2102 (X-ray single crystal diffraction). 3.1.15.3. Yb–Mn–Sb. Rühl and Jeitschko (1979) reported the results of an X-ray powder investigation of the YbMn2 Sb2 compound, CaAl2 Si2 type, a = 0.4522, c = 0.7439. For the experimental details, see EuMn2Sb2 . Yb14 MnSb11 crystallizes with the Ca14 AlSb11 structure type: a = 1.6615, c = 2.1948 after Chan et al. (1998) from X-ray single crystal diffraction. A single crystal was obtained by heating a mixture of elements to 1273–1473 K for 5–10 days and cooling the reaction to room temperature at a rate of 60 ◦ C/h. The starting materials were: dendritic Yb metal 99.999%; Sb 99.9999%; Mn ﬂakes 99.98%. 3.1.15.4. Yb–Ni–Sb. YbNiSb belongs to the MgAgAs type structure with a = 0.6238 (Dwight, 1974), from an X-ray powder analysis. For the sample preparation, ScNiSb.

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3.1.15.5. Yb–Cu–Sb. YbCuSb2 was found to form the HfCuSi2 type structure with lattice parameters of a = 0.43229, c = 0.9689 (Sologub et al., 1994). For experimental details, see LaNiSb2 . The LiGaGe type structure was established for the YbCuSb compound (a = 0.4452, c = 0.7995) by Merlo et al. (1990) by the means of powder and single crystal diffraction data of a sample obtained by melting stoichiometric amounts of the components in iron or in tantalum crucibles and arc welded shut under an argon atmosphere. After slow cooling, no further thermal treatments were applied. The purities of the metals were: Yb 99.9%, Cu and Sb 99.999%. At variance with these data, the ZrBeSi structure type was reported for the YbCuSb compound, a = 0.4456, c = 0.8006 by Flandorfer et al. (1997) from a sample prepared by high frequency melting of the components in a sealed Ta-crucible and annealed at 723 K for 168 h and ﬁnally quenched in cold water. 3.1.15.6. Yb–Zn–Sb. YbZn2Sb2 with the CaAl2 Si2 type of structure (a = 0.4444, c = 0.7424; X-ray powder diffraction data) was observed by Klüfers et al. (1980) from an alloy melted in a corundum crucible at 1173–1373 K for 4–6 hours and annealed at 1373–1473 K for 4–48 hours. The crystal structure was reﬁned by Salamakha and Mudryi (2001b) from an alloy obtained by a powder metallurgical reaction, a = 0.444194, c = 0.741913. The proper amounts of the respective powders were compacted and sealed in an evacuated silica capsule. After slowly heating to 870 K, the pellet was reground under C6 H12 , recompacted and annealed at 870 K for 400 h. The purity of starting materials was 99.9 wt.%. According to Fisher et al. (2000), Yb14 ZnSb11 compound crystallized in the Ca14 AlSb11 structure type: a = 1.6562, c = 2.1859. The single crystal was grown from a Sn ﬂux. Sologub et al. (2001) conﬁrmed the crystal structure from an alloy produced by powder reaction sintering, and they obtained slightly enlarged lattice parameters, a = 1.6615, c = 2.1948 (X-ray powder diffraction). 3.1.15.7. Yb–Se–Sb. The YbSe4 Sb2 compound belongs to the PbS4 Bi2 structure type, a = 1.150, b = 0.400, c = 1.402 (Aliev et al., 1986). 3.1.15.8. Yb–Pd–Sb. Marazza et al. (1980) established the MgAgAs type structure with a = 0.6471 for the YbPdSb compound by using X-ray powder diffraction and metallographic analyses. For the sample preparation and the purity of starting components, see Y–Pd–Sb system. YbPd2 Sb was reported to be isotypic with the crystal structure of MnCu2 Al with a lattice parameter a = 0.6669 (Riani et al., 1995) from powder diffraction data of an induction melted alloy. 3.1.15.9. Yb–Cd–Sb. Salamakha and Mudryi (2001b) observed the YbCd2 Sb2 compound and reﬁned its crystal structure from X-ray powder diffraction data, CeAl2 Si2 type structure, a = 0.46494, c = 0.75673. For the synthesis, see YbZn2Sb2 .

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3.1.15.10. Yb–Ag–Sb. The TiNiSi type structure was established for the YbAgSb compound (a = 0.7668, b = 0.4596, c = 0.8353) by Merlo et al. (1990) by the means of powder and single crystal diffraction data on a sample obtained by melting stoichiometric amounts of the components in iron or in tantalum crucibles and arc welded shut under an argon atmosphere. After slow cooling, no further thermal treatments were applied. Purities of the metals were Yb 99.9%, Ag and Sb 99.999%. The formation and crystal structure of this compound was conﬁrmed by Sologub et al. (1995a) from an arc melted and annealed at 870 K alloy by X-ray powder diffraction data and also by Flandorfer et al. (1997). 3.1.15.11. Yb–In–Sb. The ternary Yb5 In2 Sb6 compound was obtained from a direct element combination reaction in a sealed graphite tube at 973 K, and its crystal structure was determined by X-ray single crystal diffraction methods. It crystallizes in the Ba5 In2 Sb6 structure type with a unit cell of a = 0.73992, b = 2.3001, c = 0.45139 (Kim et al., 2000). 3.1.15.12. Yb–Te–Sb. Aliev et al. (1985) constructed the complete c–T diagrams for the Sb2 Te3 –Sb3 Yb4 , Sb2 Te3 –Yb, Sb4 Te7 Yb–Te and Sb4 Te7 Yb–Yb sections. The Sb2 Te3 –TeYb section was studied by Aliev and Rustamov (1978) and Rustamov et al. (1981a). Three ternary phases were observed by X-ray powder diffraction method for samples annealed at 673–773 K: Sb2 Te4 Yb, Th3 P4 structure type, a = 1.040; Sb4 Te7 Yb, Th3 P4 structure type, a = 1.0625; (YbTe)x (Te3 Sb2 )1−x , x = 0–0.06, Te3 Bi2 structure type, a = 0.425– 0.425, c = 3.020–3.038. 3.1.15.13. Yb–Pt–Sb. An early investigation of the YbPtSb compound showed that it had the MgAgAs-type with a = 0.647 (Dwight, 1974) from X-ray powder analysis. For the sample preparation, see ScNiSb. 3.1.15.14. Yb–Au–Sb. The LiGaGe type was established for the YbAuSb compound (a = 0.4635, c = 0.7765) by Merlo et al. (1990) by means of powder and single crystal diffraction method on a sample obtained by melting stoichiometric amounts of the components in iron or in tantalum crucibles and arc welded shut under an argon atmosphere. After slow cooling, no further thermal treatments were applied. The purities of the metals were: Yb 99.9%, Au and Sb 99.999%. The crystal structure was conﬁrmed by Flandorfer et al. (1997) by X-ray powder diffraction. 3.1.16. Lu–M–Sb systems 3.1.16.1. Lu–Ni–Sb. Mozharivskyj and Kuz’ma (1996) investigated the crystal structure of Lu5 Ni2 Sb (Mo5B2 Si type, a = 0.7429, c = 1.3190; X-ray powder diffraction). The alloy was prepared in the same manner as Y5 Ni2 Sb. The starting materials were: Lu not less than 99.8 wt.%, Ni and Sb 99.9 wt.%. An early investigation of the LuNiSb compound showed that it had the MgAgAs-type with a = 0.6219 (Dwight, 1974) from X-ray powder analysis. For the sample preparation, ScNiSb. Pecharsky et al. (1983a) and Hartjes and Jeitschko (1995) conﬁrmed the crystal structure and

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obtained the lattice parameters of a = 0.6187 and a = 0.6218, respectively, by X-ray powder diffraction. For experimental details, see ScNiSb and LaNiSb, respectively. 3.1.16.2. Lu–Cu–Sb. LuCuSb2 was found to form the HfCuSi2 type structure with lattice parameters of a = 0.42347, c = 0.9705 (Sologub et al., 1994) from an arc melted alloy. The materials used were: Lu 99.9%, Cu 99.9%, and Sb 99.9%. 3.1.16.3. Lu–Zr–Sb. Morozkin and Sviridov (2001) investigated the crystal structure of the LuZrSb compound by using X-ray powder diffraction. The CeScSi structure type was reported, a = 0.4178, c = 1.5952. 3.1.16.4. Lu–Pd–Sb. Mozharivskyj and Franzen (2000b) investigated the crystal structure of the Lu5 Pd2 Sb compound from an arc melted and annealed at 1070 K for 10 days alloy by using X-ray powder diffraction. The Mo5 B2 Si structure type was established, a = 0.75531, c = 1.3345. 3.1.16.5. Lu–Ag–Sb. The formation of LuAgSb compound with TiNiSi type was observed by Sologub et al. (1995a) from an arc melted and annealed at 870 K alloy by using X-ray powder diffraction. 3.1.16.6. Lu–Pt–Sb. The X-ray powder diffraction analysis of the LuPtSb compound showed that it had the MgAgAs type structure with a = 0.6457 (Dwight, 1974). For the sample preparation, see ScNiSb. Mozharivskyj and Franzen (2001) reported the crystal structure for the Lu5 Pt2 Sb compound from X-ray powder diffraction data: Mo5 B2 Si type structure, which is an ordered version of the Cr5 B3 structure type, a = 0.7519, c = 1.3326. For the experimental procedure, see Y5 Pt2 Sb. 3.1.16.7. Lu–Au–Sb. The Y3 Au3 Sb4 type structure was reported by Dwight (1977) for the Lu3 Au3 Sb4 alloy (a = 0.9723; X-ray powder diffraction). The conditions of synthesis were not speciﬁed. 3.2. R–R –Sb systems The ternary R–R –Sb systems have been studied mostly with respect to the formation of compounds with speciﬁc compositions and structures (see table 3). Ternary Nd–Pr–Sb alloys were studied by Riani et al. (1993) by using X-ray powder diffraction, and optical and electron microscopy of the samples prepared by induction melting of mixtures of the elements in small tantalum crucibles sealed by welding shut under argon. (Nd, Pr)2 Sb (La2 Sb type), (Nd, Pr)4 Sb3 (anti-Th3P4 type), (Nd, Pr)Sb (NaCl type) and (Nd, Pr)Sb2 (SmSb2 type) show complete solubility between Nd and Pr. The variation of the lattice parameters as a function of the Nd to Pr ratio was determined. The alloy Nd0.475Pr0.475Sb0.05 was investigated by differential thermal analysis; thermal effects were

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O.L. SOLOGUB AND P.S. SALAMAKHA Table 3 Crystallographic characteristics of the compounds of the R–R –Sb systems

Compound

Structure type

Space group

La3 YSb3 Yb3 DySb3 Eu3 GdSb3 Sm3 NdSb3 Sm3 GdSb3 Yb3 GdSb3

anti-Th3 P4 anti-Th3 P4 anti-Th3 P4 anti-Th3 P4 anti-Th3 P4 anti-Th3 P4

I43d I43d I43d I43d I43d I43d

Lattice parameters, nm a 0.9553 0.9333 0.8868 0.935 0.930 0.936

References Hulliger and Ott, 1977 Gambino, 1967 Gambino, 1967 Gambino, 1967 Gambino, 1967 Gambino, 1967

observed at 1090 K and 1170 K corresponding to the eutectoid (βR → R + R2 Sb) and eutectic (L → βR + R2 Sb) reactions respectively. Abulkhaev et al. (1989) reported the formation of continuous solid solutions Gdx R5−x Sb3 when R = Y, Tb, Dy, Ho with the structure of Mn5 Si3 type which originated at the isotypic binary compounds. 3.3. R–U–Sb systems R–U–Sb. A NaCl structure type was observed for continuous solid solution Y1−x Ux Sb alloys, x = 0–1, a = 0.6165–0.6208 by using X-ray powder diffraction method (Frick et al., 1984). Schmidt and Jeitschko (1998) reported the crystallographic data for the (R,U)3 Sb7 , R = Gd, Tb, Dy, Ho (table 4) and (R,U)Sb2 , R = Ce–Sm, Gd–Tm (table 5). Table 4 Lattice parameters for the (R,U)3 Sb7 (R = Gd, Tb, Dy, Ho) compounds, space group Immm Compound Gd2.31 U0.69 Sb7 Gd1.5 U1.5 Sb7 Tb1.5 U1.5 Sb7 Dy1.5 U1.5 Sb7 Ho1.47 U1.53 Sb7

a 0.4102 0.4114 0.4110 0.4103 0.4101

b 1.4643 1.4532 1.4517 1.4500 1.4477

c 1.8370 1.8252 1.8234 1.8268 1.8212

Table 5 Lattice parameters for the (R,U)Sb2 (R = Ce–Sm, Gd–Tm) compounds, space group Pnma Compound Ce0.33 U0.67 Sb2 Pr0.33 U0.67 Sb2 Nd0.33 U0.67 Sb2 Sm0.33 U0.67 Sb2 Gd0.32 U0.68 Sb2 Tb0.33 U0.67 Sb2 Dy0.33 U0.67 Sb2 Ho0.33 U0.67 Sb2 Er0.33 U0.67 Sb2 Tm0.33 U0.67 Sb2

a 0.7582 0.7582 0.7579 0.7553 0.7546 0.7546 0.7543 0.7539 0.7533 0.7531

b 0.4237 0.4231 0.4225 0.4203 0.4196 0.4186 0.4183 0.4179 0.4179 0.4172

c 1.0348 1.0323 1.0317 1.0274 1.0257 1.0242 1.0236 1.0231 1.0219 1.0209

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Table 6 Lattice parameters of the Ce1−x Lax RhSb alloys, TiNiSi type structure Composition CeRhSb Ce1−x Lax RhSb x = 0.1 Ce1−x Lax RhSb x = 0.2 Ce1−x Lax RhSb x = 0.4 Ce1−x Lax RhSb x = 0.6 Ce1−x Lax RhSb x = 0.8 LaRhSb

a 0.742 0.743 0.7455 0.747 0.7502 0.7521 0.7541

Lattice parameters, nm b 0.469 0.4626 0.4626 0.4636 0.4639 0.4648 0.4658

c 0.7859 0.7869 0.7876 0.7888 0.7892 0.7905 0.7924

Table 7 Crystallographic data for the EuCu1.75 As2 –EuCu2 Sb2 alloys Composition

Structure type

EuCu1.75 As2 EuCu1.8 As1.5 Sb0.5 EuCu1.85 AsSb EuCu1.9 As0.85 Sb1.15 EuCu2 As0.65 Sb1.35 EuCu2 As0.6 Sb1.4 EuCu2 As0.5 Sb1.5 EuCu2 Sb2

ThCr2 Si2 ThCr2 Si2 ThCr2 Si2 ThCr2 Si2 CaBe2 Ge2 CaBe2 Ge2 CaBe2 Ge2 CaBe2 Ge2

Lattice parameters, nm a c 0.4215 1.0185 0.4277 1.0368 0.4349 1.0534 0.4360 1.0579 0.4407 1.0619 0.4410 1.0614 0.4433 1.0644 0.4501 1.0824

Slovyanskikh et al. (1990) established the lattice parameters a = 13.67, b = 11.59, c = 7.26, and the space group P21 21 2 for GdU2 Sb6 .

4. Quaternary systems Substitution of Ce by La in Ce1−x Lax RhSb, x = 0.1–1.0, TiNiSi type structure (table 6) was investigated by Malik et al. (1995) in the course of studying of some of the physical properties of these phases. Dunner et al. (1995) investigated the crystallographic characteristics of the alloys with modiﬁed BaAl4 type structures within the EuCu1.75As2 –EuCu2 Sb2 region (table 7).

5. Structure types of the ternary antimonides LaFe4 P12 structure type. See ﬁg. 21, table 8. SG Im3, Z = 2, a = 0.9300 nm for NdOs4 Sb12 (Evers et al., 1995). Ce2 Pd9 Sb3 structure type. See table 9. SG Cmcm, Z = 8, a = 1.3769, b = 0.80412, c = 0.93482 (Gordon et al., 1996).

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Fig. 21. Projection of the NdOs4 Sb12 unit cell and coordination polyhedra of atoms. Table 8 Atom Nd Os Sb

Wyckoff notation 2(a) 8(c) 24(g)

x/a 0 1/4 0

y/b 0 1/4 0.34021

z/c 0 1/4 0.15591

G, % 100 100 100

Table 9 Atom Ce1 Pd1 Pd2 Pd3 Pd4 Sb1 Sb2

Wyckoff notation 8(g) 16(h) 8(f) 4(c) 8(g) 4(a) 8(e)

x/a 0.34547 0.17109 0 0 0.09840 0 0.32369

y/b 0.32828 0.17061 0.3323 0.1457 0.4582 0 0

z/c 1/4 0.08478 0.5268 1/4 1/4 0 0

G, % 100 100 100 100 100 100 100

z/c 0.1527 0.0517 1/2 0 0.3895 1/4

G, % 100 100 100 100 100 100

Table 10 Atom Nd1 Fe1 Fe2 Fe3 Sb1 Sb2

Wyckoff notation 2(a) 8(g) 2(b) 2(a) 4(e) 4(d)

x/a 0 0 0 0 0 0

y/b 0 1/2 0 0 0 1/2

NdFe3 Sb2 structure type. See ﬁg. 22, table 10. SG I4/mmm, Z = 4, a = 0.42879, c = 2.57048 (Leithe-Jasper, 1994). LaLi3 Sb2 structure type. See table 11. SG P3m1, Z = 1, a = 0.4619, c = 0.7445 (Grund et al., 1984).

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Fig. 22. Projection of the NdFe3 Sb2 unit cell and coordination polyhedra of atoms. Table 11 Atom La Li1 Li2 Sb

Wyckoff notation 1(a) 2(d) 1(b) 2(d)

x/a 0 1/3 0 1/3

y/b 0 2/3 0 2/3

z/c 0 0.658 1/2 0.2577

G, % 100 100 100 100

Fig. 23. Projection of the Ce3 Pd6 Sb5 unit cell and coordination polyhedra of atoms.

Ce3 Pd6 Sb5 structure type. See ﬁg. 23, table 12. SG Pmmn, Z = 2, a = 1.3481, b = 0.4459, c = 1.0050 nm (Gordon et al., 1995).

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O.L. SOLOGUB AND P.S. SALAMAKHA Table 12

Atom Ce1 Ce2 Pd1 Pd2 Pd3 Pd4 Sb1 Sb2 Sb3

Wyckoff notation 2(a) 4(f) 4(f) 2(b) 4(f) 2(b) 4(f) 4(f) 2(a)

x/a 1/4 0.57480 0.41109 1/4 0.56761 1/4 0.37627 0.58653 1/4

y/b 1/4 1/4 1/4 3/4 1/4 3/4 1/4 1/4 1/4

z/c 0.75756 0.75467 0.00819 0.01545 0.39730 0.47745 0.47697 0.13700 0.16899

G, % 100 100 100 100 100 100 100 100 100

Fig. 24. Projection of the YbZn2 Sb2 unit cell and coordination polyhedra of atoms. Table 13 Atom Yb Zn Sb

Wyckoff notation 1(a) 2(d) 2(d)

x/a 0 1/3 1/3

Atom La X1 X2

Wyckoff notation 2(a) 4(d) 4(e)

x/a 0 0 0

y/b 0 2/3 2/3

z/c 0 0.3619 0.7407

G, % 100 100 100

z/c 0 1/4 0.383

G, % 100 100 100

Table 14 y/b 0 1/2 0

X1 = 0.83Sb + 0.17Ni X2 = 0.17Sb + 0.83Ni

CaAl2 Si2 structure type. See ﬁg. 24, table 13. SG P3m1, Z = 1, a = 0.444194, c = 0.741913 nm for YbZn2 Sb2 (Salamakha and Mudryi, 2001b). BaAl4 structure type. See table 14. SG I4/mmm, Z = 2, a = 0.4433, c = 1.0024 nm for LaNi2 Sb2 (Pecharsky et al., 1981).

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Fig. 25. Projection of the EuNi1.53 Sb2 unit cell and coordination polyhedra of atoms. Table 15 Atom Eu Ni Sb

Wyckoff notation 2(a) 4(d) 4(e)

x/a 0 0 0

y/b 0 1/2 0

z/c 0 1/4 0.35895

G, % 100 76.6 99.5

Fig. 26. Projection of the LaNi1.51 Ge2 unit cell and coordination polyhedra of atoms.

CeGa2 Al2 structure type. See ﬁg. 25, table 15. SG I4/mmm, Z = 2, a = 0.4340, c = 1.0597 nm for EuNi1.53Sb2 (Hoffman and Jeitschko, 1988). CaBe2 Ge2 structure type. See ﬁg. 26, table 16. SG P4/nmm, Z = 2, a = 0.4466, c = 0.9918 nm for LaNi1.51Sb2 (Hoffman and Jeitschko, 1988).

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O.L. SOLOGUB AND P.S. SALAMAKHA Table 16

Atom La Ni1 Ni2 Sb1 Sb2

Wyckoff notation 2(c) 2(a) 2(c) 2(b) 2(c)

x/a 1/4 3/4 1/4 3/4 1/4

y/b 1/4 1/4 1/4 1/4 1/4

z/c 0.74000 0 0.368 1/2 0.12653

G, % 100 89.8 61.2 100 100

Fig. 27. Projection of the CeNi2.36 Sb1.64 unit cell and coordination polyhedra of atoms.

Table 17 Atom Ce X1 X2

Wyckoff notation 2(a) 4(j) 4(i)

x/a 0 1/2 0

y/b 0 0 0

z/c 0 0.256 0.3800

G, % 100 100 100

X = 0.59Ni + 0.41Sb

LaPt2 Ge2 structure type. SG P21m, Z = 2, a = 0.4365, b = 0.4355, c = 0.9969 nm, β = 90.20◦ for PrNi2 Sb2 (Slebarski et al., 1996). Atomic coordinates have not been determined. CeNi2+x Sb2-x structure type. See ﬁg. 27, table 17. SG Immm, Z = 2, a = 0.4285, b = 0.4312, c = 1.0205 for CeNi2.36 Sb1.64 (Pecharsky et al., 1982). NdFe2 Sb2 structure type. See ﬁg. 28, table 18. SG Imm2, Z = 2, a = 0.42965, b = 0.42759, c = 2.57887 (Leithe-Jasper, 1994). Ce8 Pd24Sb structure type. See table 19. SG Pm3m, Z = 1, a = 0.8461 nm (Gordon and DiSalvo, 1996).

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Fig. 28. Projection of the NdFe2 Sb2 unit cell and coordination polyhedra of atoms.

Table 18 Atom Nd1 Nd2 Sb1 Sb2 Sb3 Sb4 Fe1 Fe2 Fe3 Fe4

Wyckoff notation 2(a) 2(a) 2(a) 2(a) 2(b) 2(b) 2(a) 2(a) 2(b) 2(b)

x/a 0 0 0 0 1/2 1/2 0 0 1/2 1/2

y/b 0 0 0 0 0 0 0 0 0 0

z/c 0.1526 0.8462 0.3888 0.6109 1/4 0.7499 0.5044 0.0105 0.0513 0.4490

G, % 100 100 100 100 100 100 100 100 100 100

z/c 0.25140 1/2 0 0 1/4

G, % 100 100 100 100 100

z/c 0 1/2 1/4

G, % 100 100 100

Table 19 Atom Ce1 Pd1 Pd2 Pd3 Sb

Wyckoff notation 8(g) 6(f) 6(e) 12(h) 1(a)

x/a 0.25140 0.25552 0.31118 0.26675 0

y/b 0.25140 1/2 0 1/2 0

Table 20 Atom Y Sb Pd

Wyckoff notation 4(a) 4(b) 8(c)

x/a 0 1/2 1/4

y/b 0 1/2 1/4

MnCu2 Al structure type. See table 20. SG Fm3m, Z = 4, a = 0.6691 nm for YPd2 Sb (Ishikawa et al., 1982).

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Fig. 29. Projection of the CeAgSb2 unit cell and coordination polyhedra of atoms. Table 21 Atom Ce Ag Sb1 Sb2

Wyckoff notation 2(c) 2(b) 2(a) 2(c)

x/a 1/4 3/4 3/4 1/4

Atom La Zn Sb1 Sb2

Wyckoff notation 2(a) 2(b) 2(b) 2(a)

x/a 1/4 1/4 3/4 1/4

Atom La In Sb1 Sb2

Wyckoff notation 2(e) 2(e) 2(e) 2(e)

x/a 0.8440 0.2139 0.6158 0.2489

y/b 1/4 1/4 1/4 1/4

z/c 0.23788 1/2 0 0.67363

G, % 100 99 100 100

y/b 1/4 3/4 1/4 1/4

z/c 0.74071 0.00299 0.49962 0.15410

G, % 100 60 100 100

z/c 0.2160 0.4846 0.6951 0.0016

G, % 100 81 100 100

Table 22

Table 23 y/b 1/4 1/4 1/4 1/4

HfCuSi2 structure type. See ﬁg. 29, table 21. SG P4/nmm, Z = 2, a = 0.43641, c = 1.0722 nm for CeAgSb2 (Sologub et al., 1995a). NdAgAs2 structure type. See table 22, SG Pmmn, Z = 2, a = 0.437935, b = 0.440222, c = 1.050438 nm for LaZnSb2 (Salamakha and Mudryi, 2001a). LaInSb2 structure type. See table 23. SG P21/m, Z = 2, a = 0.4521, b = 0.4331, c = 1.1913 nm, β = 99.66◦ (Ferguson et al., 1999).

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Table 24 Atom La Sb1 Sb2 Sn1 Sn2 Sn3

Wyckoff notation 4(c) 4(c) 4(c) 8(f) 4(c) 4(a)

x/a 0 0 0 0 0 0

y/b 0.86085 0.24860 0.59076 0.0065 0.0089 0

z/c 1/4 1/4 1/4 0.1238 1/4 0

G, % 100 81 100 18.6 18.6 19.7

Fig. 30. Projection of the La6 MnSb15 unit cell and coordination polyhedra of atoms.

LaSnx Sb2 (x = 0.75) structure type. See table 24. SG Cmcm, Z = 4, a = 0.42435, b = 2.3121, c = 0.45053 nm (Ferguson et al., 1996). La6 MnSb15 structure type. See ﬁg. 30, table 25. SG Imm2, Z = 2, a = 1.51538, b = 1.93646, c = 0.427422 nm for Ce6 Mn0.4 Sb15 (Sologub et al., 1996b). La6 Ge5-x Sb11+x structure type. See table 26. SG Immm, Z = 2, a = 0.43034, b = 1.0851, c = 27.073 nm (Lam et al., 2001).

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O.L. SOLOGUB AND P.S. SALAMAKHA Table 25

Atom Ce1 Ce2 Mn Sb1 Sb2 Sb3 Sb4 Sb5 Sb6

Wyckoff notation 8(e) 4(d) 4(c) 8(e) 8(e) 4(d) 4(c) 4(c) 2(a)

Atom La1 La2 Sb1 Sb2 Sb3 Sb4 Sb5 X1 X2

Wyckoff notation 4(i) 8(l) 4(j) 8(l) 4(g) 4(f) 4(f) 8(l) 4(g)

x/a 0.1408 0 0.2751 0.2139 0.3595 0 0.1603 0.4066 0

y/b 0.1322 0.3232 0 0.2979 0.1062 0.1968 0 0 0

z/c 0.0787 0.0787 0.0787 0.0787 0.0787 0.5787 0.5787 0.5787 0.0000

G, % 100 100 40 100 100 100 100 100 100

y/b 0 0.19435 0 0.30535 0.29207 1/2 0 0.1205 0.03926

z/c 0. 26676 0.40544 0.35768 0.28862 0 0 0.07187 0.14765 0

G, % 100 100 100 100 100 50 100 100 50

z/c 1/2 1/2 0 0.443 0.0663 0 0 1/2 0

G, % 100 100 86 47 47 100 100 100 100

Table 26 x/a 0 0 1/2 0 0 0.4300 1/2 0 0

X1 = 61% Ge + 39% Sb X2 = 19% Ge + 31% Sb Table 27 Atom La1 La2 La3 Ga1 Ga2 Sb1 Sb2 Sb3 Sb4

Wyckoff notation 6(m) 6(m) 1a 12(n) 4(h) 6(l) 6(j) 6(k) 3(f)

x/a 0.58274 0.16800 0 0.1343 1/3 0.24818 0.24697 0.37508 1/2

y/b 0.16547 0.33600 0 0 2/3 0.49636 0 0 0

La13 Ga8 Sb21 structure type. See table 27. SG P6/mmm, Z = 1, a = 1.7657, c = 0.43378 nm (Mills and Mar, 2000). Pr12 Ga4 Sb23 structure type. See table 28. SG Immm, Z = 2, a = 0.42162, b = 1.94070, c = 2.63972 nm (Mills and Mar, 2000). Nd6 Fe13Si structure type. See ﬁg. 31, table 29. SG I4/mcm, Z = 4, a = 0.80978, c = 2.32317 nm for Nd6 Fe13 Sb (Leithe-Jasper, 1994).

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Table 28 Atom Pr1 Pr2 Pr3 Pr4 Ga1 Ga2 Ga3 Sb1 Sb2 Sb3 Sb4 Sb5 Sb6 Sb7 Sb8

Wyckoff notation 8(l) 8(l) 4(j) 4(j) 4(i) 4(h) 4(g) 8(l) 8(l) 8(l) 8(l) 4(i) 4(h) 4(g) 2(a)

x/a 0 0 1/2 1/2 0 0 0 0 0 0 0 0 0 0 0

y/b 0.27695 0.38900 0 0 0 0.181 0.43337 0.11138 0.11584 0.22151 0.33456 0 0.38335 0.23336 0

z/c 0.40559 0.26312 0.09340 0.38118 0.18986 1/2 0 0.43300 0.14030 0.28669 0.14421 0.28911 1/2 0 0

G, % 100 100 100 100 96 2.7 100 97.3 100 100 100 100 100 100 100

Fig. 31. Projection of the Nd6 Fe13 Sb unit cell and coordination polyhedra of atoms.

Table 29 Atom Nd1 Nd2 Fe1 Fe2 Fe3 Fe4 Sb

Wyckoff notation 16(l) 8(f) 16(l) 16(l) 16(k) 4(d) 4(a)

x/a 0.1691 0 0.3824 0.1767 0.0652 0 0

y/b 0.6691 0 0.8824 0.6767 0.2103 1/2 0

z/c 0.18595 0.39777 0.0917 0.0557 0 0 1/4

G, % 100 100 100 100 100 100 100

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O.L. SOLOGUB AND P.S. SALAMAKHA

Fig. 32. Projection of the Ce3 Au3 Sb4 unit cell and coordination polyhedra of atoms. Table 30 Atom Ce Au Sb

Wyckoff notation 12(a) 12(b) 16(c)

x/a 3/8 7/8 0.0844

y/b 0 0 0.0844

z/c 1/4 1/4 0.0844

G, % 100 100 100

z/c 0 1/2

G, % 100 100

Table 31 Atom Sm X

Wyckoff notation 1(a) 2(d)

x/a 0 1/3

y/b 0 2/3

X = 0.5Ni + 0.5Sb

Y3 Au3 Sb4 structure type. See ﬁg. 32, table 30. SG I43d, Z = 4, a = 1.00443 for Ce3 Au3 Sb4 (Sologub et al., 1998). AlB2 structure type. See ﬁg. 33, table 31. SG P6/mmm, Z = 1, a = 0.4372, c = 0.3843 nm for SmNiSb (Pecharsky et al., 1983a, 1983b). ZrBeSi structure type. See ﬁg. 34, table 32. SG P63 /mmc, a = 0.4404, c = 0.8403 nm for LaNiSb (Hartjes and Jeitschko, 1995). CaIn2 structure type. See table 33. SG P63 /mmc, Z = 2, a = 0.4580, c = 0.7716 for NdPdSb (Marazza et al., 1980).

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Fig. 33. Projection of the SmNiSb unit cell and coordination polyhedra of atoms.

Fig. 34. Projection of the LaNiSb unit cell and coordination polyhedra of atoms.

Table 32 Atom La Ni Sb

Wyckoff notation 2(a) 2(c) 2(d)

x/a 0 1/3 1/3

Atom Nd X

Wyckoff notation 2(b) 4(f)

x/a 0 1/3

y/b 0 2/3 2/3

z/c 0 1/4 3/4

G, % 100 100 100

y/b 0 2/3

z/c 0.25 0.04

G, % 100 100

Table 33

X = 0.5Pd + 0.5Sb

NdPtSb (or LiGaGe) structure type. See ﬁg. 35, table 34. SG P63 mc, Z = 2, a = 0.4534, c = 0.7866 nm (Wenski and Mewis, 1986a).

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Fig. 35. Projection of the NdPtSb (or LiGaGe) unit cell and coordination polyhedra of atoms.

Table 34 Atom Nd Pt Sb

Wyckoff notation 2(a) 2(b) 2(b)

x/a 0 1/3 1/3

y/b 0 2/3 2/3

z/c 0.000 0.7137 0.2635

G, % 100 100 100

Fig. 36. Projection of the YZrSb unit cell and coordination polyhedra of atoms.

KHg2 structure type. SG Imma Z = 4, a = 0.4584, b = 0.7329, c = 0.7838 nm for NdRhSb (Malik and Adroja, 1991b). Atomic coordinates have not been determined. CeScSi structure type. See ﬁg. 36, table 35. SG I4/mmm, Z = 4, a = 0.4245, c = 1.6306 nm for YZrSb (Morozkin and Sviridov, 2001).

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Table 35 Atom Y Zr Sb

Wyckoff notation 4(e) 4(c) 4(e)

x/a 0 0 0

y/b 0 1/2 0

z/c 0.335 0 0.143

G, % 100 100 100

y/b 1/4 1/4 1/4

z/c 0.7008 0.4172 0.0900

G, % 100 96.6 100

Table 36 Atom Ce Rh Sb

Wyckoff notation 4(c) 4(c) 4(c)

x/a 0.0118 0.2997 0.1908

Fig. 37. Projection of the ScNiSb unit cell and coordination polyhedra of atoms. Table 37 Atom Sc Ni Sb

Wyckoff notation 4(b) 4(c) 4(a)

x/a 1/2 1/4 0

Atom Ce Ge Sb1 Sb2

Wyckoff notation 4(g) 2(d) 2(b) 4(h)

x/a 0.1406 0 1/2 0.3047

y/b 1/2 1/4 0

z/c 1/2 1/4 0

G, % 100 100 100

z/c 0 0 0 1/2

G, % 100 100 100 100

Table 38 y/b 0 0 0 0

TiNiSi structure type. See table 36. SG Pnma, Z = 4, a = 0.7581, b = 0.4642, c = 0.7893nm for CeRhSb (Salamakha et al., 2000). MgAgAs structure type. See ﬁg. 37, table 37. SG F43m, Z = 4, a = 0.6055 nm for ScNiSb (Pecharsky et al., 1983a, 1983b). Te2 Ag3 Tl structure type. See ﬁg. 38, table 38. SG Cmmm, Z = 4, a = 1.8894, b = 0.4650, c = 0.4299 for Ce2 GeSb3 (Stetskiv et al., 1998).

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Fig. 38. Projection of the Ce2 GeSb3 unit cell and coordination polyhedra of atoms. Table 39 Atom La Ti Sb1 Sb2

Wyckoff notation 6(g) 2(b) 6(g) 4(d)

x/a 0.6176 0 0.2507 1/3

Atom La1 La2 Mg1 Mg2 Mg3 Sb1 Sb2 Sb3 Sb4

Wyckoff notation 2(d) 2(c) 2(d) 2(d) 1(b) 2(d) 2(d) 2(d) 1(a)

x/a 1/3 0 1/3 1/3 0 1/3 1/3 1/3 0

y/b 0 0 0 2/3

z/c 1/4 0 1/4 0

G, % 100 100 100 100

z/c 0.07041 0.21173 0.4031 0.6733 1/2 0.28754 0.56417 0.85691 0

G, % 100 100 83 100 82 100 100 100 100

Table 40 y/b 2/3 0 2/3 2/3 0 2/3 2/3 2/3 0

U3 CrSb5 structure type (Hf5 CuSb3 -anti type). See table 39. SG P63 /mcm, Z = 2, a = 0.95294, c = 0.62801 nm for La3 TiSb5 (Bollore et al., 1995). La4 Mg5-x Sb7 structure type. See table 40. SG P3m1, Z = 1, a = 0.46201, c = 2.6069 for La4 Mg4.48Sb7 structure (Ganguli et al., 1993). La5-y Mg2-x Sb6 structure type. See table 41. SG R3m, Z = 3, a = 0.4616, c = 6.767 for La4.89Mg1.539Sb6 (Ganguli et al., 1993). La3 Mg5-x Sb6 structure type. See table 42. SG R3m, Z = 3, a = 0.4625, c = 6.691 for La3 Mg4.6 Sb6 (Ganguli et al., 1993).

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Table 41 Atom La1 La2 La3 Mg Sb1 Sb2 Sb3

Wyckoff notation 6(c) 6(c) 3(a) 6(c) 6(c) 6(c) 6(c)

x/a 0 0 0 0 0 0 0

Atom La1 La2 Mg1 Mg2 Mg3 Sb1 Sb2 Sb3

Wyckoff notation 6(c) 3(a) 6(c) 6(c) 3(b) 6(c) 6(c) 6(c)

x/a 0 0 0 0 0 0 0 0

y/b 0 0 0 0 0 0 0

z/c 0.27869 0.44266 0 0.15230 0.08289 0.19509 0.36087

G, % 100 94.5 100 83.0 100 100 100

y/b 0 0 0 0 0 0 0 0

z/c 0.38795 0 0.12927 0.23407 1/2 0.08404 0.19154 0.30550

G, % 100 100 90 100 80 100 100 100

Table 42

Table 43 Atom Eu1 Eu2 Eu3 Eu4 Mn Sb1 Sb2 Sb3 Sb4

Wyckoff notation 16(e) 32(g) 32(g) 32(g) 8(a) 8(b) 16(f) 32(g) 32(g)

x/a 1/4 0.9565 0.9786 0.1808 0 0 0.1332 0.0034 0.8685

y/b 0.6432 0.6768 0.8741 0.1589 0 0 0.1332 0.8614 0.7244

z/c 1/8 0.9528 0.1260 0.9679 0 1/4 1/4 0.9374 0.0783

G, % 100 100 100 100 100 100 100 100 100

Ca14 AlSb11 structure type. See table 43. SG I41/acd, Z = 8, a = 1.7300, c = 2.2746 nm for Eu14 MnSb11 (Rehr and Kauzlarich, 1994). Ba5 Al2 Sb6 structure type. See table 44. SG Pbam, Z = 2, a = 0.73992, b = 2.3001, c = 0.45139 nm for Yb5 In2 Sb6 (Mills and Mar, 2000). La3 InGe structure type. SG I4/mcm, Z = 16, a = 1.2012, c = 1.5485 nm for Ce3 GeSb (Stetskiv et al., 1998). Atomic coordinates have not been determined. Mo5 B2 Si structure type. See table 45. SG I4/mcm, Z = 4, a = 0.7593, c = 1.3258 nm for Dy5 Ni2 Sb (Mozharivskyj and Kuz’ma, 1996).

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O.L. SOLOGUB AND P.S. SALAMAKHA Table 44

Atom Yb1 Yb2 Yb3 In Sb1 Sb2 Sb3

x/a 0.9584 0.0269 1/2 0.3244 0.5465 0.05465 0.1989

y/b 0.0895 0.2446 0 0.1202 0.1369 0.1897 0.9992

G, % 100 100 100 100 100 100 100

z/c 1/2 1/2 1/2 0 0 0 0

Table 45 Atom Dy1 Dy2 Ni Sb

Wyckoff notation 4(c) 16(i) 8(h) 4(a)

x/a 0 0.1597 0.372 0

y/b 0 0.6597 0.872 0

z/c 0 0.1385 0 1/4

G, % 100 100 100 100

6. Physical properties of the ternary antimonides 6.1. RM 2 Sb2 compounds The CeNi2 Sb2 compound was classiﬁed as Kondo system by Kaczmarska et al. (1993) from magnetic properties and resistivity measurements. The resistivity shows a maximum at 2.5 K and a minimum at 28 K (ﬁg. 39). As reported by Skolozdra et al. (1994), it has a Curie–Weiss

Fig. 39. Resistivity vs T for LaNi2 Sb2 and CeNi2 Sb2 .

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Fig. 40. χ in emu/g and 1/χ in (emu/mole)−1 vs T for PrNi1.8 Sb2 .

temperature θp of −28 K, TN = 2.5 K and μeff = 2.60μB . The residual resistivity of LaNi2 Sb2 is 80 μ cm after Kaczmarska et al. (1993). Slebarski et al. (1996) measured the magnetic properties for the PrM2 Sb2 compounds (ﬁg. 40–42: TN = 6.24 K, θp = −4.0 K, μeff = 3.60μB , Hcr = 10.0 kOe at T = 4.2 for PrNi1.8 Sb2 (ﬁg. 40); TN = 6.5 K, θp = −3.5 K, μeff = 3.58μB , Hcr = 10.3 kOe at T = 4.2 for PrNi2 Sb2 (ﬁg. 41); TN = 6.0 K, θp = −1.5 K, μeff = 3.51μB , Hcr 1.0 kOe at T = 4.2 for PrCu2 Sb2 (ﬁg. 42). It was found from magnetic susceptibility measurements that Pr is nearly trivalent. Guzik and Pierre (1998) presented the magnetotransport properties of LaCu2 Sb2 (ﬁg. 43), LaAg2 Sb2 (ﬁg. 43) and CeAg2 Sb2 compounds (ﬁg. 44). The resistivity of CeAg2 Sb2 exhibits a very broad plateau from room temperature down to 100 K then a slight increase down to 20 K followed by a sharp drop at the Néel temperature 9 K. Skolozdra et al. (1994) reported Kondo-like behavior for the resistivity of CeCu2 Sb2 , with a maximum at 17 K and a minimum at about 140 K of (ﬁg. 45) and θp = −7 K, TN = 3 K and μeff = 2.60μB . Gordon et al. (1995) reported the physical properties of Ce3 Pd6 Sb5 . The magnetic susceptibility exhibits signiﬁcant anisotropy with an effective high temperature momentum per Ce of 2.67μB and antiferromagnetic ordering at 6 K. The resistance shows a minimum near 17 K and an anomaly at 6 K.

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Fig. 41. χ in emu/g and 1/χ in (emu/mole)−1 vs T for PrNi2 Sb2 .

Fig. 42. χ in emu/g and 1/χ in (emu/mole)−1 vs T for PrCu2 Sb2 .

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Fig. 43. Resistivity of LaCu2 Sb2 and LaAg2 Sb2 .

Fig. 44. Resistivity of CeAg2 Sb2 .

6.2. RNiSb compounds Hartjes and Jeitschko (1995) measured the magnetic characteristics of the RNiSb compounds (table 46). It was observed that the magnetic susceptibility of LaNiSb is nearly temperature independent. The average value of the susceptibility for the temperature range between 100

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O.L. SOLOGUB AND P.S. SALAMAKHA

Fig. 45. Resistivity of CeCu2 Sb2 (right hand scale) and CeCuSb2 (left hand scale). Table 46 Magnetic properties of RNiSb compounds (Hartjes and Jeitschko, 1995) Compound

Structure type

μexp (μB )

LaNiSb CeNiSb PrNiSb NdNiSb SmNiSb GdNiSb TbNiSb DyNiSb HoNiSb ErNiSb TmNiSb LuNiSb

ZrBeSi ZrBeSi ZrBeSi ZrBeSi ZrBeSi MgAgAs MgAgAs MgAgAs MgAgAs MgAgAs MgAgAs MgAgAs

0 2.59(5) 3.68(4) 3.68(4) 1.58(8) 8.1(5) 10.2(4) 10.6(4) 10.7(4) 9.5(3) 7.6(3) 0

μeff (R 3+ ) (μB ) (theory) 0 2.54 3.58 3.62 1.60 7.94 9.72 10.63 10.60 9.59 7.57 0

θ (K) – −9(1) 0(1) 16(2) – −15(5) −13(2) −6(2) 0(3) 0(2) 0(1) –

Type of magnetism Pauli paramagnetic Curie–Weiss Curie–Weiss Curie–Weiss Van Vleck paramagnetic Curie–Weiss Curie–Weiss Curie–Weiss Curie–Weiss Curie–Weiss Curie–Weiss Pauli paramagnetic

and 300 K is χ = 1.8 × (±0.1) × 10−9 m3 /mol which is typical for the Pauli paramagnetism of metallic conductors. The lutetium compound is also assumed to be Pauli paramagnetic. The magnetic susceptibilities between 250 and 300 K are equally small as they are for LaNiSb. It

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Fig. 46. Resistivity vs temperature for CeNiSb.

was also reported in the same work that for compounds with magnetic lanthanide elements, the magnetism is dominated by the magnetic moments of these elements. The samarium compound shows van Vleck paramagnetism. All other compounds exhibit Curie–Weiss behavior. The magnetism and resistivity of CeNiSb were investigated by Skolozdra et al. (1994). The susceptibility of CeNiSb follows a Curie–Weiss law above 35 K, with an effective moment of 2.70(5)μB and a Curie–Weiss temperature of ∼15 K. However, susceptibility deviates from this law at lowest temperatures, and diverges near TC = 7 K, where spontaneous magnetization appears. The ferromagnetic moment reaches 0.48μB at 1.5 K. The resistivity exhibits a maximum at about 60 K and a minimum around 200 K (ﬁg. 46). A kink in the curve occurs at 7 K, which conﬁrms the Curie temperature. The maximum slope of resistivity vs temperature is reached near 15 K. The magnetoresistance at low temperature is negative. The initial slope is vanishing small in the paramagnetic range, and negative in the ferromagnetic state. Based on these results, the authors announced CeNiSb to be a new ferromagnetic Kondo system. In contrast to this investigation, measurements on a sample in the later work performed by Hartjes and Jeitschko (1995) show a normal Curie–Weiss behavior, and the effective magnetic moment calculated from the linear portion of the 1/χ vs T plot above 50 K of μexp = 2.59(5)μB

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O.L. SOLOGUB AND P.S. SALAMAKHA

which is in good agreement with the theoretically expected effective moment for a free Ce3+ ion of 2.54μB . Magnetic susceptibility and electrical resistivity measurements on CePdSb and GdPdSb were carried out in the temperature range of 4.2–300 K by Malik and Adroja (1991a). The measurements reveal that CePdSb orders ferromagnetically with an ordering temperature of 17 K while GdPdSb orders antiferromagnetically with a Néel temperature of 15.5 K. In the paramagnetic state, the susceptibility of CePdSb follows Curie–Weiss behavior between 50 and 300 K but deviates from it below 50 K. Its saturation magnetic moment per formula unit at 4.2 K is 1.2μB which is reduced from the free ion value of 2.14μB for the Ce3+ ion. The resistivity of CePdSb shows a broad maximum at about 150 K and a ln(T ) behavior at high temperatures, indicating the combined inﬂuence of crystalline electric ﬁelds and the Kondo effect on the 4f moments. Thus the authors suggest that CePdSb is a Kondo-lattice system with ferromagnetic ordering of cerium moments. The compound CeRhSb, which crystallizes in the orthorhombic CeCu2 -type structure, has been synthesized by Malik and Adroja (1991b). Its unit-cell volume is anomalous in relation to that of the isostructural RRhSb compounds. Its magnetic susceptibility is weakly temperature dependent and exhibits a broad maximum at about 113 K, characteristic of valence-ﬂuctuating Ce compounds. The resistivity also shows a broad maximum at 113 K followed by a rapid rise below 21 K. The latter indicates gap formation in the electronic density of states. The gap energy is estimated to be about 4 K. Thus CeRhSb appears to represent a valence ﬂuctuating cerium compound in which a pseudogap develops in the electronic density of states at low temperatures. Adroja et al. (1999) performed the neutron scattering studies on CeRhSb and PrMSb (M = Rh, Pd). Aliev et al. (1988) reported the results of transport and magnetic measurements of RNiSb, R = Sc, Er, Ho, Tm, Yb. It was suggested that the gap in the electron energy spectrum in these systems is due to the speciﬁc crystal structure with a vacancy in the Ni sublattice. It was found that properties of RNiM compounds are strongly inﬂuenced by the annealing process. Preliminary results on low temperature transport properties in YbPdSb system with MgAgAs type structure are presented by Aliev et al. (1988). Resistivity shows a maximum at T = 50–100 K and the Fermi-liquid decrease of ≈ 0 + AT 2 at helium temperatures. The high value of the A coefﬁcient 5 μ cm/K2 indicates the possibility of the heavy fermion behavior with γ about 300–400 mJ/mol K2 . The Seebeck coefﬁcient S is positive and shows a maximum Smax ≈ 22 μV/K at T ≈ 200 K. The electrical resistivity, magnetic susceptibility and magnetization for YbTSb compounds (T = Cu, Ag, Au) were measured by Katoh et al. (1997); the results are presented in table 47 and ﬁg. 47. Also, Flandorfer et al. (1997) classiﬁed the YbCuSb and YbAgSb compounds as temperature independent Pauli-type paramagnets whereas a small magnetic moment ≈ 1μB was observed for YbAuSb. From X-ray absorption spectroscopy at 10 and 300 K, Yb was determined to be dipositive with temperature independent valences for all compounds: 2.06 for M = Ag, 2.08 for M = Cu and 2.14 for M = Au.

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Table 47 Fitting parameters of magnetic susceptibility and electrical resistivity of YbT Sb: C, Curie constant; θP , paramagnetic Curie temperature; χ0 , temperature independent susceptibility; χC , diamagnetic susceptibility; R, high temperature slope; θR , characteristic temperature, 0 , residual resistivity Compound YbCuSb YbAgSb YbAuSb

C, e.m.u.Kmol−1 0.0376 0.00245 0.00339

θP , K −35.8 −4.42 −4.37

χ0 , e.m.u.mol−1 1.38 × 10−4 −7.69 × 10−5 −8.47 × 10−5

χC , e.m.u.mol−1 −4.9 × 10−5 −6.1 × 10−5 −7.7 × 10−5

R, μ cm K−1 0.44 0.26 0.21

θR , K 170 150 140

0 , μ cm 260 46 48

Fig. 47. Electrical resistivity vs for YbT Sb compounds (T = Cu, Ag, Au).

6.3. RMSb2 compounds The magnetic data on the RM1−x Sb2 (R = La, Ce, Pr, Nd and Sm and M = Mn, Zn) compounds are summarized in table 48 (Sologub et al., 1995a). The magnetic behavior of the RMnSb2 compounds is characterized by the onset of ferromagnetism of the Mn sublattice in the temperature range between 100 and 520 K. Ordering of the rare earth sublattice below 50 K was observed for samples containing Ce, Pr and Nd. CeZnSb2 remains paramagnetic over the temperature range investigated (4.2–550 K). From isothermal magnetization data at 5 K (ﬁg. 48) the magnetic structures of the RM1−x Sb2 phases (R = La, Ce, Pr, Nd and Sm) were thought to be rather complex (metamagnetism). The magnetic susceptibilities of the RMSb2 (M = Ni, Pd, Cu, Au) phases were generally measured over the temperature range from 4 K to 100 K (Sologub et al., 1994) (table 49, ﬁgs. 49, 50). YCuSb2 and LaMSb2 are temperature independent paramagnets. The RMSb2 compounds are found to order antiferromagnetically below T = 20 K. PrPdSb2 and TbPdSb2 undergo metamagnetic transitions, whereas PrCuSb2 and ErCuSb2 are simple fer-

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O.L. SOLOGUB AND P.S. SALAMAKHA Table 48 Magnetic characteristics for the RMn1−x Sb2 compounds, M = Mn, Zn

Compound LaMn0.87 Sb2 CeMn0.85 Sb2 PrMn0.82 Sb2 a NdMn0.83 Sb2 SmMn0.90 Sb2 a CeZn1−x Sb2

Tc (K) ∼ 310 ∼ 310 ∼ 390 ∼ 250 ∼ 250

σ (μa ) 0.8b 1.2c 1.0c 0.6c 0.4b

θ p (K) 228 104

μeff/f.u (μB ) 4.6 4.8

μeff/Mn (μB ) 4.6 4.3

225

5.5

4.5

−11

2.6

a Multiphase samples. b T = 5 K, H = 2 Tesla. c T = 5 K, H = 3 Tesla.

Fig. 48. Magnetization vs magnetic ﬁeld for RMn1−x Sb2 after Sologub et al. (1995a, 1995b, 1995c).

romagnets. The Sm-containing compounds are typical Van Vleck paramagnets owing to the closely spaced multiplets. According to Skolozdra et al. (1994), the resistivity for CeCuSb2 shows a maximum at 7 K and a minimum at 70 K, as for concentrated Kondo systems (ﬁg. 45). The resistivity of LaCuSb2 is that of a classical metallic system. The La0.4Ce0.6 CuSb2 solid solution alloy exhibits a strong increase of the resistivity at low temperature similar to that of the pure compound with a maximum at 9 K. The magnetoresistance has been measured for the CeCuSb2 up to 5 T; a huge drop of resistivity is observed under a magnetic ﬁeld. The summary of magnetic properties of CeCuSb2 , CeNiSb2 and (Ce1−x Lax )CuSb2 obtained by Skolozdra et al.

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Table 49 Magnetic characteristics of the RMSb2 compounds, M = Ni, Pd, Cu, Au (Sologub et al., 1994) Compound LaNiSb2 CeNiSb2 PrNiSb2 NdNiSb2 SmNiSb2 GdNiSb2 TbNiSb2 DyNiSb2 HoNiSb2 LaPdSb2 CePdSb2 PrPdSb2 NdPdSb2 SmPdSb2 GdPdSb2 TbPdSb2 YCuSb2 LaCuSb2 CeCuSb2 PrCuSb2 NdCuSb2 SmCuSb2 GdCuSb2 TbCuSb2 DyCuSb2 HoCuSb2 ErCuSb2 TmCuSb2 LaAuSb2 CeAuSb2 PrAuSb2 NdAuSb2 SmAuSb2

TN (K) TIP < 4.0 6.0 < 4.0 9.0 12.0 10.0 < 4.0 TIP < 4.0 8.0b < 4.0

θ p (K) 0.0 −4.0 −12.0 −44.0 −44.0 −27.0 −12.0 −65.0 −13.0 −30.

15.0 18.0b TIP TIP 8.0 5.0c < 4.0

−41.0 −30.0

12.0 9.0 6.0 < 4.0 < 4.0d < 4.0 TIP 6.0 9.0 < 4.0

−33.0 −23.0 −9.0 −4.0 −3.0 −3.0

−7.0 3.5 −9.0

2.0 −6.0 −9.6

μeff (μB ) 1.44 4.00 4.30 1.80a 9.60 10.80 12.00 10.20 3.04 4.00 3.50 1.50a 7.90 9.80

2.50 3.60 3.70 1.30a 8.90 9.40 10.30 10.40 9.80 7.30 2.30 3.90 3.40 1.50c

TIP temperature independent paramagnet. a Effective moment at 80 K. b Metamagnetism, μ H 0 crit > 2.5 T. c Ferromagnetic, magnetic moment (μ H = 3 T at 5 K) = 1.7μ . B 0 d Ferromagnetic, magnetic moment (μ H = 3 T at 5 K) = 5.6μ . B 0

(1994) are presented in table 50, and the reciprocal magnetic susceptibility of the ﬁrst and last compounds is shown in ﬁg. 51. Vijaya Lakshmi et al. (1996) performed magnetic and electrical resistivity measurements on LaMSb2 and CeMSb2 , M = Ni, Cu (see ﬁg. 52). CeNiSb2 orders ferromagnetically at 6 K while CeCuSb2 orders antiferromagnetically at 5 K. The electrical resistivity of the two La compounds, LaCuSb2 and LaNiSb2 show normal metallic behavior down to 5.4 K with no

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O.L. SOLOGUB AND P.S. SALAMAKHA

Fig. 49. Molar susceptibility vs T for the RMSb2 , M = Ni, Pd, Cu after Sologub et al. (1994).

Fig. 50. Molar susceptibility vs T for the RAuSb2 , R = Ce, Pr after Sologub et al. (1994).

Table 50 Magnetic characteristics of the RMSb2 compounds, M = Ni, Cu (Skolozdra et al., 1994) Compound CeCuSb2 CeNiSb2 Ce0.8 La0.2 CuSb2 Ce0.6 La0.4 CuSb2

μeff (μB ) 2.57 2.45 2.59 2.59

θ p (K) −11 +6 −12 −11

Tc , TN (K) 7 7 4 <2

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123

Fig. 51. 1/χ vs T for CeCuSb2 and (Ce1−x Lax )CuSb2 after Skolozdra et al. (1994).

superconducting transitions. The resistivity of CeCuSb2 and CeNiSb2 show broad minimum typical for Kondo lattice systems. There is a low temperature drop in resistivity in both the compounds due to magnetic ordering. In CeNiSb2 a second minimum (at 10 K) followed by a maximum at 6 K is also observed. All compounds except CeNiSb2 exhibit positive magnetoresistance in the temperature range 1.5–4.5 K in ﬁelds up to 45 kOe. The CeNiSb2 compound shows negative magnetoresistance. Accordingly to Sologub et al. (1995a), magnetism of the RAgSb2 phases over the 2.5 to 300 K temperature range is characterized by tripositive paramagnetic behavior of the lanthanide atoms (table 51, ﬁg. 53). RAgSb2 with R = Y, La are weakly temperature dependent paramagnets. In contrast, RAgSb2 compounds with R = Pr, Nd, Sm, Gd, Dy, Ho, Er, Tm are weak antiferromagnets with ordering temperatures lower than TN ∼ 13 K, and CeAgSb2 is a noncolinear antiferromagnet (TM ∼ 12 K) with a remanent magnetization μ = 0.15μB per Ce atom. André et al. (2000) reported results of neutron diffraction measurements performed on RAgSb2 (R = Ce, Pr, Nd, Tb, Dy, Ho, Er, Tm). All compounds were found to be collinear antiferromagnets with the Néel temperature between 2.0 K (for TmAgSb2) and 11.1 K (for

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O.L. SOLOGUB AND P.S. SALAMAKHA

Fig. 52. Resistivity vs T for LaCuSb2 , CeCuSb2 , LaNiSb2 and CeNiSb2 after Vijaya Lakshmi et al. (1996).

TbAgSb2), except for CeAgSb2 which is a ferromagnet with a Ce magnetic moment equal to 0.33μB and parallel to the c-axis. Thermal expansion, magnetostriction and magnetic susceptibility under pressure have been measured on a polycrystalline CeAgSb2 sample by Thornton et al. (1999). It was observed that in zero magnetic ﬁeld the magnetic contribution to the linear thermal expansion coefﬁcient

b

c

d 125

Fig. 53. 1/χ vs T for RAgSb2 , R = Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm.

RARE EARTH – ANTIMONY SYSTEMS

a

126

f

g

h Fig. 53. Continued

O.L. SOLOGUB AND P.S. SALAMAKHA

e

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127

i

j

Fig. 53. Continued

has a broad maximum near 17 K with the value of 7.9 × 10−6 K−1 but there is no peak at the TN = 9.5 K. TN was found to decrease under pressure at the rate −10.1 Mbar−1 . Flandorfer et al. (1996) reported on the magnetic properties of CeFe0.6 Sb2 : TM = 9.5 K, θp = −23 K, μeff/f.u. = 2.6μB . Magnetic characteristics for the CeM1−x Sb2 compounds, M = Mn, Ni, Pd, Cu, Ag, Au, Zn were also measured (ﬁg. 54). The LIII absorption edge measurements were performed on the CeMSb2 compounds, M = Fe, Co, Ni, Pd, Cu, Ag and Au at 10 K and 300 K. The LIII absorption edge spectra are similar at both temperatures and show that Ce in all compounds is in the trivalent, or nearly trivalent state. 6.4. R 3 M 3 Sb4 compounds Shaked et al. (1979) reported on the results of magnetic susceptibilities measurements on the R3 Au3 Sb4 compounds (R = Tb, Ho, Er and Tm) between 4 and 300 K (table 52, ﬁg. 55). The compounds were found to be paramagnetic down to 4 K. Electrical resistivity, Hall constant, magnetic susceptibility and speciﬁc heat measurements were performed on the R3 Au3 Sb4 (R = La, Ce, Pr) and the R3 Pt3 Sb4 (R = Ce, Pr) com-

128

O.L. SOLOGUB AND P.S. SALAMAKHA Table 51 Magnetic data of ternary RAgSb2 compounds Compound YAgSb2 LaAgSb2 CeAgSb2 PrAgSb2 NdAgSb2 SmAgSb2 GdAgSb2 TbAgSb2 DyAgSb2 HoAgSb2 ErAgSb2 TmAgSb2

TN (K) χ0 = 0.7 × 10−6 cm3 g−1 χ0 = 0.6 × 10−6 cm3 g−1 12.0a 4.3 4.4 10.0 14.0 13.0 12.0 6.0 4.8 3.1

θ p (K)

μeff (μB )

−6 −2 −9 −41 −35 −14 −12 −6 −6 −8

2.57 3.61 3.91 0.8b 7.8 9.6 10.5 10.3c 9.4 7.5

Note. Error limits on TN , θ p and μeff are ±0.5 K, ±1 K and ±0.05μB , respectively. a Noncolinear antiferromagnet, remanent magnetization μ = 0.15μ /Ce. B b χ = 1.8 × 10−6 cm3 g−1 . 0 c Corrected for ∼15 mole% of excess free (Sb) in the alloy.

Fig. 54. Reciprocal susceptibility for the CeM1−x Sb2 , M = Mn, Fe, Ni, Pd, Cu, Ag, Au, Zn.

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129

Fig. 55. 1/χ vs T for R3 Au3 Sb4 , R = Tb, Ho, Er, Tm after Shaked et al. (1979).

Table 52 The experimental effective magnetic moment of the R3 Au3 Sb4 compounds (R = Tb, Ho, Er and Tm) at 300 K after Shaked et al. (1979) μeff. (μB )

Tb3+ 8.94

Ho3+ 9.30

Er3+ 9.42

Tm3+ 6.91

pounds by Kasaya et al. (1991). La3 Au3 Sb4 and Ce3 Au3 Sb4 show semi-metallic or semiconducting behaviors whereas Pr3 Pt3 Sb4 shows a metallic one. The valence of the Ce ions in Ce3 Au3 Sb4 is 3+. The results indicate that R3 Au3 Sb4 and R3 Pt3 Sb4 are narrow-gap semiconductors and metals respectively. Ce3 Pt3 Sb4 shows semiconducting behavior and that the Ce ions are in a mixed valence state. Magnetic susceptibility and inverse magnetic susceptibility vs T curves for Ce3 Au3 Sb4 and Ce3 Pt3 Sb4 are presented in ﬁg. 56.

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O.L. SOLOGUB AND P.S. SALAMAKHA

Fig. 56. χ and 1/χ vs T for Ce3 Au3 Sb4 and Ce3 Pt3 Sb4 after Kasaya et al. (1991).

R3 Au3 Sb4 (R = Sm, Gd) showed semi-metallic behaviors (Katoh and Kasaya, 1993). They are antiferromagnets with TN of 2 and 11 K, respectively. The same authors observed no magnetic transitions down to 1.5 K in Ce3 Au3 Sb4 and found C/T = 2500 mJ/mol K2 at 1.5 K which makes this compound a heavy Fermion material. The (T ) curves for R3 Au3 Sb4 (R = La, Ce, Pr, Sm, Gd) given by Katoh and Kasaya (1993) are presented in ﬁgs. 57 and 58. Kimura et al. (1995) reported on an investigation of the electronic structure of R3 Au3 Sb4 (R = La, Ce, Pr) by reﬂectivity and resonant photoemission spectra. The hybridization between the Ce4f state and the Sb5p state valence band was found to be weak as deduced from the resonant photoemission spectra of Ce3 Au3 Sb4 . This result was found to be consistent with the electronic structure derived from an analysis of the optical data about the energy gap.

RARE EARTH – ANTIMONY SYSTEMS

131

Fig. 57. vs T for Ce3 Au3 Sb4 .

Fig. 58. vs T for R3 Au3 Sb4 (R = La, Pr, Sm, Gd).

Resistivity, magnetic susceptibility, speciﬁc heat and inelastic neutron scattering were measured for Ce3 Au3 Sb4 by Kasaya et al. (1994). The compound was found to be a semiconductor with a resistivity of 22 cm at 0.13 K. Magnetic susceptibility and inelastic neutron scattering show that 4f electrons are in the localized 4f1 state. No anomaly in the thermomagnetic curve down to 0.5 K has been observed. However, there exist a broad peak at 1.5 K in the speciﬁc heat at C/T ∼ 2500 mJ/mole K2 and the peak, which is symmetrical in a log T plot, shifts towards higher temperature values under the inﬂuence of a magnetic ﬁeld.

132

O.L. SOLOGUB AND P.S. SALAMAKHA

Fig. 59. Temperature dependence of the electrical resistivity for Ce3 Au3 Sb4 and Ce3 Pt3 Sb4 after Katoh and Kasaya (1996).

Fig. 60. Temperature dependence of the electrical resistivity for Ce3 Au3−x Ptx Sb4 (x = 0.5, 1.0, 1.5, 2.25).

Kasaya et al. (1994) and Katoh and Kasaya (1996) measured the electrical resistivity, Hall constant and magnetic susceptibility for the Ce3 Au3−x Ptx Sb4 (x = 0.0, 0.5, 1.0, 1.5, 2.25, 3.0) (ﬁgs. 59, 60, table 53). Resistivity and magnetic susceptibility were studied for the R3 Cu3 Sb4 compounds (R = Y, La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er) by Skolozdra et al. (1993) (table 54). Resistivity measurements indicates that all compounds are semiconductors. A linear (T ) dependence was observed for Y3 Cu3 Sb4 , Nd3 Cu3 Sb4 and Gd3 Cu3 Sb4 while for Ce3 Cu3 Sb4 a minima was observed at ∼250 K. The temperature dependence of the magnetic susceptibility χ(T ) for R3 Cu3 Sb4 , R = Ce, Pr, Nd, Gd, Tb, Dy, Er can be described by the Curie–Weiss law with

RARE EARTH – ANTIMONY SYSTEMS

133

Table 53 Magnetic data for Ce3 Au3−x Ptx Sb4 compounds (x = 0.0, 0.5, 1.0, 1.5, 2.25, 3.0) Compound Ce3 Au3 Sb4 Ce3 Au2.5 Pt0.5 Sb4 Ce3 Au2 PtSb4 Ce3 Au1.5 Pt1.5 Sb4 Ce3 Au0.75 Pt2.25 Sb4 Ce3 Pt3 Sb4

Temperature range 150 ∼ 300 150 ∼ 300 80 ∼ 300 170 ∼ 300 480 ∼ 720 450 ∼ 700

C, emu/mole K 0.79 0.807 0.822 0.837 0.868 1.083

θ p (K) -2.86 -11.0 -45.6 -100 -236 -647

μeff (μB ) 2.51 2.54 2.56 2.59 2.63 2.94

Table 54 Magnetic data for the R3 Cu3 Sb4 (Skolozdra et al., 1993) Compound Ce3 Cu3 Sb4 Pr3 Cu3 Sb4 Nd3 Cu3 Sb4 Gd3 Cu3 Sb4 Tb3 Cu3 Sb4 Dy3 Cu3 Sb4 Ho3 Cu3 Sb4 Er3 Cu3 Sb4

θ p (K) 10 11 11 59 −10 −7 3 24

μeff (μB /atom R) 2.59 3.31 3.61 7.72 9.96 11.02 11.11 9.50

the values of the effective magnetic moments close to that of the free R 3+ ions. La3 Cu3 Sb4 and Y3 Cu3 Sb4 are diamagnets. For Sm3 Cu3 Sb4 , the χ(T ) curve does not obey the Curie– Weiss law. Ce3 Cu3 Sb4 was found to be a semiconducting ferromagnet with ferromagnetic transition temperature, Tm = 10 T while Gd3 Cu3 Sb4 was reported to be a metallic antiferromagnet with TN = 12 K (Patil et al., 1996). Patil et al. (1998) reported on measurements of magnetic susceptibility, electrical resistivity and magnetoresistivity for the Ce3 Rh3 Sb4 in the temperature range 2 K to 300 K. The compound was found to order antiferromagnetically at 22 K. The magnetic resistivity shows a broad maximum at about 50 K. 6.5. R6 MSb15 compounds Magnetic measurements were performed down to liquid helium temperature by Sologub et al. (1996a) for R = Ce, Pr, Sm, Gd and M = Mn, Zn (table 55, ﬁg. 61). Ce6 MnSb15 and Gd6 ZnSb15 undergo an antiferromagnetic transition at 7 and 15 K respectively. Ce6 ZnSb15 and Pr6 ZnSb15 remain paramagnetic in the temperature range investigated, whereas Sm6 ZnSb15 is a van Vleck-type paramagnet. Magnetic and transport properties have been measured by Deakin et al. (2001) for the series of ternary rare-earth antimonides R6 Ge5−x Sb11+x (R = La–Nd, Sm, Gd–Dy) (table 56). All are metallic, with the members containing R, other than La, displaying kinks in their resistivity vs temperature curves. Tb and Dy containing compounds exhibit Kondo-like behavior with resistivity minima occurring at 10 and 150 K, respectively. The R6 Ge5−x Sb11+x (R = Ce–

134

O.L. SOLOGUB AND P.S. SALAMAKHA Table 55 Magnetic data of the ternary R6 MSb15 compounds

Compound Ce6 MnSb15 Ce6 ZnSb15 Pr6 ZnSb15 Sm6 ZnSb15 Gd6 ZnSb15

TN (K) 7

15

θ p (K) −6 −10 −13 9 −34

μeff.meas. (μB ) 8.9 2.7 3.6 0.5 7.7

μeff.theor. (μB ) 2.54 2.54 3.6 7.9

Fig. 61. Reciprocal magnetic susceptibility vs temperature for Ce6 MSb15 , M = Mn, Zn. Inset: Molar susceptibility vs temperature for Ce6 MnSb15 .

Nd, Sm, Gd) members exhibit residual resistivity ratios (300 K /2 K ) close to 2.0, consistent with the partial disorder of Ge and Sb found in the crystal structure of these phases. For the compounds with R = Ce, Pr, Nd, Sm, Gd, Tb, the magnetic susceptibility and electrical resistivity measurements reveal long-range antiferromagnetic ordering with TN 22 K. At 2 K, the Ce, Pr, and Nd members undergo metamagnetic transitions at critical ﬁelds between 1.0 and 4.0 T, while the Gd containing compound shows spin-ﬂop behavior with HSF = 1.85 T and HC = 5.75 T. 6.6. R 14 MSb11 compounds Eu14 MnSb11 was reported to be an intermetallic colossal magnetoresistive material having a metal insulator transition associated with a ferromagnetic phase transition at 92 K (Chan et al., 1997). Temperature dependent dc susceptibility measurements were performed on the Yb14ZnSb11 compound in an applied ﬁeld of 1 kOe in the [100], [110] and [001] directions (Fisher et al., 2000). For temperatures above approximately 150 K, the susceptibility follows a Curie–Weiss

RARE EARTH – ANTIMONY SYSTEMS

135

Table 56 Summary of the resistivity and magnetism data for the R6 Ge5−x Sb11+x compounds Compound

300 K /2 K

La6 Ge5−x Sb11+x Ce6 Ge5−x Sb11+x Pr6 Ge5−x Sb11+x Nd6 Ge5−x Sb11+x Sm6 Ge5−x Sb11+x Gd6 Ge5−x Sb11+x Tb6 Ge5−x Sb11+x Dy6 Ge5−x Sb11+x

2.18 2.23 2.03 1.70 2.05 1.77 1.46 0.92

μeff (300 K) (μB /R 3+ )

μRS (μB /R 3+ )

θ (K)

TN (K)

2.58 3.54 3.94 1.2 7.08 8.53

2.54 3.58 3.62 0.85 7.94 9.72

−27 −8 −53

4.0 2.7 4.2 8.3 12.5 22

−47 −10

HSF (2 K) (T)

HC (2 K) (T) 1.0 1.5 4.0

1.85

5.75 >7

temperature dependence with Curie constants (4.63, 4.13 and 5.68) ±0.04 × 10−4 emu K/g and Weiss constants (−223, −294 and −474) ±10 K for the ﬁeld parallel to [100], [110] and [001] directions, respectively. An intermediate Yb valence behavior with a spin ﬂuctuating temperature of approximately 85 K was determined from thermodynamic, magnetic and transport measurement data. The resistivity of Yb14 AlSb11 is typical of many Zintl compounds and indicates that this material is a small gap semiconductor or a semimetal in contrast to the more metallic behavior of Yb14 ZnSb11 and Yb14 MnSb11 (Fisher et al., 2000). 7. Peculiarities of the interaction of the rare earths and antimony 7.1. Binary systems Similar to other binary R–p-element systems, the formation of binary rare earth – antimonides with a simple stoichiometry is a characteristic feature of these systems. The largest number of structure types formed was encountered for the group of RSb2 compounds (4 members). The polymorphic modiﬁcations were observed for GdSb2 and TbSb2 as well as the RSb (R = La, Ce) and R5 Sb3 (R = Yb, Y and Sc) compounds were noted to undergo the solid state transformations. Although the phase diagrams have been constructed for all R–Sb systems except Eu and Sc, there are many reports on the crystal structure of compounds which are not shown in the corresponding phase diagram. The systematic thermochemical investigations of the rare earth antimonides (R = Y, La, Ce, Pr, Nd, Sm and Dy) and optimization of the thermodynamic data have been carried out by Cacciamani et al. (1996) and Ferro et al. (1988) respectively. Later on, the same group of authors (Borzone et al., 2000) suggested that the poor reliability of results for most of the R–Sb phase diagrams are attributable to experimental difﬁculties arising from the high melting temperatures of the compounds, the high reactivity of samples, and the high volatility of the antimony. For Gd–Sb phase diagram, as an example, the GdSb2 (66.6 at% Sb) was reported to be the richest in Sb compound with two structural modiﬁcations, SmSb2 and HoSb2 (Abdusalamova et al., 1986). In more recent work, Altmeyer and Jeitschko (1998) established the existence the Gd2 Sb5 compound (71.42 at% Sb) with the monoclinic structure of the Dy2 Sb5 type.

136

O.L. SOLOGUB AND P.S. SALAMAKHA Table 57 Isotypic compounds of the binary R–Sb systemsa

Composition R2 Sb R5 Sb3 R4 Sb3 R11 Sb10 RSb R2 Sb5 RSb2

Structure type La2 Sb Cu2 Sb Mn5 Sb3 Yb5 Sb3 anti-Th3 P4 Ho11 Ge10 NaCl HgMn Dy2 Sb5 SmSb2 HoSb2 CaSb2 ZrSi2

La

Ce

Pr

Nd

Sm

+ – + – + – + +

+ – + – + – + +

+ – + – + – +

+ – + – + – +

+ – + – + – +

+ – – –

+ – – –

+ – – –

+ – – –

+ + – – –

Eu

+

– – + –

Gd

Tb

Dy

Ho

Er

Tm

Yb

Lu

Y

Sc

– – + – + – +

– – + – + – +

– – + – + – +

– – + – + – +

– – – + + – +

– – +

– – + – – +

– – + + + – +

– + – +

– – +

– – + + + + +

+ + + – –

+ + + – –

+ – + – –

– + – –

– + – –

– + – –

– – – +

– + – –

– + – –

+

a Sign + means that the compound with corresponding structure type exists; – the compound was not observed.

Borzone et al. (2000) studying the phase diagram of Gd–Sb system, observed and determined the crystal structure of Gd16 Sb39 (70.91 at% Sb). The structures of Eu containing binary antimonides are isotypic with binary antimonides of alkaline earth metals (Ca, Ba, Sr) and do not have the analogues, except for Eu5 Sb3 , in other R–Sb systems (table 57). 7.2. Ternary systems As is evident from the foregoing paragraphs, the interaction of the components in the ternary R–M–Sb systems have not been adequately studied. The isothermal sections (over all concentration region or partially) have been constructed for the limited number of ternary systems (22), and in other systems only the samples of speciﬁc compositions were synthesized and investigated structurally with respect to the formation of isotypic compounds. This paucity of data complicates the pursuance of a proper analysis and the derivation of regularities. 7.2.1. R–s-element–Sb Few experimental data are available only for lithium and magnesium containing systems however the isothermal section is constructed for Gd–Li–Sb (5 ternary compounds have been observed). The replacement of R element in the RLi2 Sb2 compounds leads to the formation of different structure type: CaAl2 Si2 (R = Ce) → CaBe2 Ge2 (R = Pr, Nd) → unknown structure (R = Tb). No comparative analysis can be made for the magnesium containing systems since only the information regarding the existence of three compounds in the La–Mg–Sb system is presented in the literature. 7.2.2. R–p-element–Sb The isothermal sections have been constructed for the La–Al–Sb and Ce–Si(Ge)–Sb systems.

RARE EARTH – ANTIMONY SYSTEMS

137

Ternary compounds have been observed for the R–Si, Ge, Sn, Ga, In, Se, Te–Sb systems. The systems with arsenic and bismuth are characterized by formation of substitutional solid solutions between isotypic binary pnictides. No compounds have been found in the partly investigated ternary La–Al–Sb system at 773 K (Muravjova, 1971). For the Yb–Al–Sb, the formation and crystal structure of the Yb14 AlSb11 have been reported (Fisher et al., 2000). 7.2.3. R–d-element–Sb In spite of the fact that the isothermal sections have been investigated for the 18 ternary systems from 448 possible R–d-element–Sb combinations, a considerable number of publications is devoted to the crystal structure investigations of ternary compounds that enables one to consider more thoroughly the effect of R-element and d-element interaction as well as the formation, composition and crystal structure of ternary antimonides. 7.2.3.1. R–Ti(V, Cr, Zr, Nb, Mo, Hf, Ta, W, Re)–Sb. For this combination of elements, the R–Mo (Ta, W, Re)–Sb systems have not been studied, and as well no information is available on the interaction of Eu and Yb with these d-elements. The R3 MSb5 series of compounds was observed only for the light lanthanides and the RZrSb structure is typical for the yttric subgroup. The CeVSb3 type occurs in the R–V–Sb systems for the ceric subgroup and in the R–Cr–Sb systems for both subgroups (R = La–Sm, Gd–Dy) (table 58). 7.2.3.2. R–Mn(Cd, Zn)–Sb. Analysis of the compositions and crystal structures of the investigated R–3d-element–Sb systems established a vague similarity between R–Mn–Sb and the cadmium and zinc containing systems (table 59): (i) the HfCuSi2 and La6 MnSb15 structures are typical for the ceric subgroup and Gd; (ii) Eu and Yb form the CaAl2 Si2 and Ca14 AlSb11 types; (iii) no compounds have been found in the Tb–Tm, Lu and Y, Sc containing systems. 7.2.3.3. R–Fe(Co, Ru, Rh, Os, Ir)–Sb. Among the ternary R–Fe(Co, Ru, Rh, Os, Ir)–Sb systems, the Nd–Fe–Sb system is the most completely studied (Sologub and Salamakha, 1999; Table 58 Isotypic compounds of the ternary R–Ti(V, Cr, Zr, Nb, Hf)–Sb systemsa Structure type U3 CrSb5

CeVSb3 CeScSi

Ti Zr Nb Hf V Cr Zr

La + + + + + +

Ce + + + + + +

Pr + + + + + +

Nd + + + + + +

Sm + + – + + +

Eu

Gd

Tb

Dy

Ho

Er

Tm

+ +

+ +

+ +

+

+

+

Yb

Lu

Y

+

+

a Sign + means that the compound with corresponding structure type exists; – the compound was not observed.

Sc

138

O.L. SOLOGUB AND P.S. SALAMAKHA Table 59 Isotypic compounds of the ternary R–Mn(Zn, Cd)–Sb systemsa

Structure type HfCuSi2

CaAl2 Si2

Ca14 AlSb11 La6 MnSb15 NdAgSb2

Mn Zn Cd Mn Zn Cd Mn Zn Mn Zn Zn

La + + +

Ce + + + –

Pr + + +

– + + +

+ + +

+

Nd + + + – – – – – – +

Sm + + +

Eu

Gd

Tb

Dy

Ho

Er

Tm

Yb

Lu

Y

Sc

+ + + + + +

+

+ + + + + +

a Sign + means that the compound with corresponding structure type exists; – the compound was not observed.

Table 60 Isotypic compounds of the ternary R–Fe(Co, Ru, Rh, Os, Ir)–Sb systemsa Structure type HfCuSi2 LaFe4 Sb12

TiNiSi or KHg2 Nd6 Fe13 Si

Fe Co Fe Ru Rh Os Co Rh Fe Co

La + + + + + +

Ce + + + +

Pr + + + +

Nd + + + +

Sm + + + +

Eu

Gd +

Tb

Dy

Ho

Er

Tm

Yb

+ +

+

+

+

+

+

+

+ – +

+ + –

+ +

+ – + +

Lu

Y

+ +

Sc

+

a Sign + means that the compound with corresponding structure type exists; – the compound was not observed.

Leithe-Jasper, 1994). Information on the systematic investigations of the interaction of rare earths and antimony with other metals of this subgroup is still lacking. The survey of the isotypic compounds is presented in table 60. No information is available on the ternary R–Ir–Sb systems. 7.2.3.4. R–Ni(Pd, Pt)–Sb. Interaction of the components in these systems is the most complicated and highly diversiﬁed (table 61). The greatest efforts have concentrated on the systematic studies of the nickel containing systems. The annealing temperature of the R–Ni–Sb alloys strongly affects the phase equilibria as well as the crystal structure of ternary compounds. The isothermal section of Y–Ni–Sb phase diagram at 870 K (0–50 at.% Sb) was studied by Zavalii (1982). For the La–Ni–Sb, Ce– Ni–Sb and Nd–Ni–Sb systems the isothermal sections at 870 K were constructed by Zavalii (1982), Pecharsky et al. (1983a, 1983b) and Salamakha (1998), respectively. Mozharivskyj

RARE EARTH – ANTIMONY SYSTEMS

139

Table 61 Isotypic compounds of the ternary R–Ni(Pd, Pt)–Sb systemsa Structure type CeGa2 Al2 CaBe2 Ge2 AlB2 or ZrBeSi CaIn2 or LiGaGe MgAgAs

Mo5 B2 Si

HfCuSb2 MgCu2 Al TiNiSi

Ni Pd Ni Pd Ni Pd Pt Ni Pd Pt Ni Pd Pt Ni Pd Pd Pd Pt

La + – + + + + + – – – –

Ce + – + + + + + – – – –

Pr + – + + + + + – – –

Nd + – + + + + + – – – –

Sm + – + + + + – – – +

Eu + – – + – – – – – –

Gd + – +

Tb –

Dy –

Ho –

Er –

+ +

+ +

+ +

+ +

+ +

– –

– –

– –

– –

– –

Tm

Yb

+

+

+

+

– + – + – + + + + + +

– + – + + + + + + +

– – – + + + + + + +

– – – + + + + + +

+ + + +

– –

– + – + – + + + + + +

–

– – – + + +

+ +

– –

– –

+ – –

+ – –

+ – –

– –

– +

+ – –

Lu

– – – + + + + +

– –

Y

Sc

– – – + + + + + + –

–

+ – –

– + +

– –

a Sign + means that the compound with corresponding structure type exists; – the compound was not observed.

et al. (1997) investigated the phase equilibria in the ternary Ho–Ni–Sb system at 770 K (0–50 at.% Sb) and 1070 K (50–100 at.% Sb). Hoffman and Jeitschko (1988) reported some results of phase equilibria studies of the La–Ni–Sb and Gd–Ni–Sb systems at 1070 K. The compounds RNi2−x Sb2 with a defect CaBe2 Ge2 structure were found and evaluated as the highest antimony content compounds. In variance to these data, Zavalii (1982), Pecharsky et al. (1983a, 1983b) and Salamakha (1998) reported on the existence and crystal structure for the RNiSb2 (HfCuSi2 type structure) and RNi2 Sb2 (CeGa2 Al2 type structure) (R = La, Ce, Nd) compounds from the alloys annealed at 870 K. Various authors investigated the crystal structure of the RNiSb compounds (R = La–Sm) and found them to crystallize either with AlB2 type (LT form) or ZrBeSi type (HT modiﬁcation). Although no phase diagram has been studied for the Ce–Pd–Sb system, seven ternary compounds were observed and their crystal structures were investigated. In the R–Pt–Sb systems, the compounds with Y3 Au3 Sb4 structure are found for both the light and heavy rare earth elements. This structure occurs typically for copper and gold containing antimonides, and unexpectedly, it was not observed for the systems with Ni and Pd. 7.2.3.5. R–Cu(Ag, Au)–Sb. The most prevailing structure types among the compounds within R–Cu(Ag, Au)–Sb systems are the HfCuSi2 and Y3 Au3 Sb4 types. The compounds of the Y3 Au3 Sb4 type have not been observed for the systems with silver. Table 62 lists the isotypic series of compounds in the R–Cu(Ag, Au)–Sb systems.

140

O.L. SOLOGUB AND P.S. SALAMAKHA Table 62 Isotypic compounds of the ternary R–Cu(Ag, Au)–Sb systemsa

Structure type HfCuSi2

Y3 Au3 Sb4 ZrBeSi or LiGaGe La6 MnSb15 CeGa2 Al2 TiNiSi

Cu Ag Au Cu Au Cu Ag Au Cu Cu Ag Ag

La + + + + + –

Ce + + + + + –

+ – +

+ + + +

Pr + + + + +

+

Nd + + + + + – – – – – –

Sm + + + + +

Eu – –

Gd + +

Tb + +

Dy + +

Ho + +

Er + +

Tm + +

Yb + –

Lu + –

Y + +

Sc

– – + + +

+ +

+ +

+ +

+ +

+ +

– +

– – + – +

– +

+ +

– –

+

+ +

+

–

–

a Sign + means that the compound with corresponding structure type exists; – the compound was not observed.

7.2.4. R–f-element–Sb Only the formation of solid solutions between isotypic compounds has been observed in the R–R –Sb systems. For the R–U–Sb the formation of both solid solutions (Frick et al., 1984) and ternary compounds (Schmidt and Jeitschko, 1998; Slovyanskikh et al., 1990) have been reported. 7.3. Interconnection of the ternary antimonides with the binary structure types The structure types of binary antimonides have been described by Hulliger (1984) in chapter 33 of the Handbook. Several families of ternary antimonides crystallize with structure types derived from those of binary types by an insertion of third component in the structure of binary compounds, i.e., LaFe4 P12 from CoAs3 , Y3 Au3 Sb4 from Th4 P3 , U3 CrSb5 from Mn5 Si3 . Another subgroup of structure types of ternary antimonides contains the superstructures of binary structures: LiGaGe → CaIn2 , ZrBeSi → Ni2 In, Mo5 B2 Si → Cr5 B3 , MgAgAs → CaF2 , TiNiSi → Co2 Si. The structure of the MnCu2 Al type compound can be considered as both an insertion phase (NaCl) and a superstructure (BiF3 ). The crystal chemistry of the ternary antimonides is discussed in the original papers. Here we present only some regularities and peculiarities of the formation of ternary antimonides and their structures depending on the qualitative and quantitative composition. 7.4. Ternary antimonides with the equiatomic composition The RMSb compounds crystallize in eight structure types, for some of them the existence of two polymorphic modiﬁcations have been reported (table 63). The crystal structure of EuMSb compounds is always different than the structure of other RMSb compounds.

RARE EARTH – ANTIMONY SYSTEMS

141

Table 63 Structure types of the RMSb ternary antimonidesa M/R Ni Pd Pt Co Rh Cu Ag Au Zr

La 1,2 4 4

Ce 1,2 4 4

Pr 1,2 4 6

Nd 1,2 4 4,6

7

5,7

7

7

Sm 1,2 4 3

Eu 5 5

Gd 1,3 4 3

Tb 3 4 3

Dy 3 3,4 3

Ho 3 3 3

Er 3 3 3

Tm 3 3 3

2 2 2

4

Yb 3 3 3

6 5 6 8

8

8

8

8

Lu 3 3

Y 3 3 3

Sc 3 3 5

5

8

8

8

a Number 1 corresponds to AlB structure type; 2 – ZrBeSi; 3 – MgAgAs; 4 – CaIn ; 5 – TiNiSi; 6 – LiGaGe; 2 2 7 – KHg2 ; 8 – CeScSi.

7.5. Ternary antimonides with the R:Sb ratio equal to 1:2 A BaAl4 fragment is a ﬁlled up tetragonal antiprism. The structure types of ternary antimonides related to the BaAl4 type are presented in table 64. In the La(Ni, Sb)4 compound (BaAl4 structure type), the atoms of (Ni, Sb) statistical mixture occupy two different crystallographic positions. For the 1:2:2 composition, two ordered modiﬁcations of tetragonal cell – CeGa2 Al2 and CaBe2 Ge2 – are known. An orthorhombic deformation of the BaAl4 with unit cell dimensions similar to the BaAl4 -type unit cell was found for the CeNi2+x Sb2−x compound. The LaPt2 Ge2 and Ce3 Pd6 Sb5 structure types can be formed in consequence of ordering and distortion of the unit cell of the CaBe2 Ge2 structure. In the HfCuSi2 structure, a portion of the tetragonal antiprisms is unﬁlled. The outer deformation of this structure leads to the formation of two new structure types – NdAgAs2 and LaInSb2. Table 64 Structure types of antimonides with structures related to BaAl4 type structure Structure types

Space group

BaAl4 CeGa2 Al2 CaBe2 Ge2 CeNi2+x Sb2−x LaPt2 Ge2

I4/mmm I4/mmm P4/nmm Immm P21

a a1 a1 a1 a1 a1

Ce3 Pd6 Sb5 HfCuSi2 NdAgAs2 LaInSb2

Pmmn P4/nmm Pmmn P21 /m

3a1 a1 a1 a1

Lattice parameters b a1 a1 a1 a1 a1 β ∼ 91◦ a1 a1 a1 a1 β ∼ 99◦

c c1 c1 c1 c1 c1 c1 c1 c1 c1

142

O.L. SOLOGUB AND P.S. SALAMAKHA

The structure of the LaSnSb2 compound (Cmcm space group) is related to the structure of YbSb2 (ZrSi2 structure type, Cmcm space group). The structure of NdFe2 Sb2 and NdFe3 Sb2 compounds can be classiﬁed to the structures with two short (∼ 4 Å) and one much more longer period (∼ 25 Å). These structures contain the fragments of simple structures connected along long period. The insertion of additional Li atom in the 0 0 0.5 site in the structure of the RLi2 Sb2 compounds (CaAl2 Si2 structure type) leads to the formation of the YLi3 Sb2 structure type. Acknowledgement This work was partially supported by FCT grant in ITN, Portugal (P.S) and NATO Research Fellowship in ITN, Portugal (O.S.). References Abdusalamova, M.N., Rachmatov, O.I., 2000. J. Alloys Compd. 299, L1. Abdusalamova, M.N., Burnashev, O.R., Mironov, K.E., 1981. J. Less-Common Met. 77, 81. Abdusalamova, M.N., Burnashev, O.R., Mironov, K.E., 1984. J. Alloys Compd. 102, L19. Abdusalamova, M.N., Burnashev, O.R., Mironov, K.E., 1986. J. Less-Common Met. 125, 1. Abdusalamova, M.N., Rakhmatov, O.I., Fazlyeva, N.D., Tchuiko, A.C., 1988. J. Less-Common Met. 141, L23. Abdusalamova, M.N., Faslyeva, N.D., Eliseev, A.A., Shishkin, E.A., Rakhmatov, O.I., Chuiko, A.G., Shumakova, T.P., 1990. J. Less-Common Met. 166, 229. Abdusalamova, M.N., Rakhmatov, O.I., Fazlyeva, N.D., Tchuiko, A.C., 1991. Izv. Akad. Nauk SSSR, Neorg. Mater. 27 (8), 1386. Abulkhaev, V.D., Abdusalamova, M.N., 1989. Phase diagram of the system Ce–Sb. In: V Vsesoyuzn Soveshchan. “Diagrammy Sost. Metall. Sistem”, Tezisy dokl., Moskva 1989, p. 137. Abulkhaev, V.D., Abdusalamova, M.N., Chuiko, A.G., Timofeev, S.S., 1989. Conditions of formation and crystal chemistry of continuous solutions Gdx Ln5−x Sb3 (Ln = Y, Tb, Dy, Ho). In: V AllUnion Conference on the Crystal Chemistry of Intermetallic Compounds, Abstracts, Lvov, 1989, p. 123. Adroja, D.T., Rainford, B.D., Malik, S.K., Takeya, H., Gschneidner, K.A., Pecharsky, V.K., 1999. J. Alloys Compd. 288, 7. Albering, J.H., Ebel, T., Jeitschko, W., 1997. Z. Kristallogr. 12, 242.

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Handbook on the Physics and Chemistry of Rare Earths Vol. 33 edited by K.A. Gschneidner, Jr., J.-C.G. Bünzli and V.K. Pecharsky © 2003 Elsevier Science B.V. All rights reserved

Chapter 213 THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES R.J.M. KONINGS∗ and A. KOVÁCS† European Commission, Joint Research Centre, Institute for Transuranium Elements, P.O. Box 2340, 76125 Karlsruhe, Germany; E-mail: [email protected]

Contents

1. 2.

3.

4.

5.

6.

List of symbols List of acronyms Introduction Polymorphism 2.1. LnF3 2.2. LnCl3 2.3. LnBr3 2.4. LnI3 Low-temperature heat capacity and standard entropy of the solid trihalides 3.1. LnF3 3.2. LnCl3 3.3. LnBr3 and LnI3 High-temperature heat capacity of the solid trihalides 4.1. LnF3 4.2. LnCl3 4.3. LnBr3 and LnI3 Enthalpy of formation of the solid trihalides 5.1. LnF3 5.2. LnCl3 , LnBr3 and LnI3 Heat capacity of the liquid trihalides 6.1. LnF3

148 148 148 149 149 150 152 152

7.

8.

154 154 158 161

9. Appendix A.

162 162 166 168

Appendix B. Appendix C.

169 169 172 175 175

Appendix D. Appendix E.

6.2. LnCl3 6.3. LnBr3 and LnI3 Heat capacity of the gaseous trihalides 7.1. LnX 3 monomers 7.2. Ln2 X 6 dimers Enthalpy of formation of the gaseous trihalides 8.1. LnF3 8.2. LnCl3 8.3. LnBr3 8.4. LnI3 8.5. Ln2 X 6 dimers Conclusions The transition and melting points of the lanthanide trihalides The enthalpies of formation of the solid lanthanide trihalides Experimental data for the liquid trihalides Molecular parameters of the lanthanide trihalides The enthalpies of sublimation of the lanthanide trihalides References

178 180 182 182 190 191 191 193 194 196 197 198 200 209 222 224 234 241

∗ Corresponding author. † On leave from Research Group for Technical Analytical Chemistry of the Hungarian Academy of Sciences at the

Institute of General and Analytical Chemistry, Budapest University of Technology and Economics. 147

148

R.J.M. KONINGS AND A. KOVÁCS

List of symbols A

Madelung constant

Ttrs

transition temperature

Cp

heat capacity at constant pressure

U

energy

Cexs Clat

excess heat capacity lattice heat capacity

Vm Z

molar volume ionic charge

D bond energy d, f, g polarization functions

f H ◦ enthalpy of formation at 298.15 K r H ◦ enthalpy of reaction sub H enthalpy of sublimation

Q

molecular partition function

R re

universal gas constant equilibrium bond distance

rg

thermal average distance at the temperature of

trs S ◦ entropy of transition

ra

the ED experiment distance between average nuclear positions at a

ε ν1

electronic energy symmetric stretch

trs H ◦ enthalpy of transition fus S ◦ entropy of fusion

given temperature

ν2

symmetric bend (inversion)

S◦ T

standard entropy temperature

ν3 ν4

asymmetric stretch asymmetric bend

Tfus

fusion temperature

List of acronyms (aq)

aqueous

(g)

gas

BP

Becke–Perdew86 exchange-correlation func-

IR

infrared spectroscopy

B3P

tional (Perdew, 1986; Becke, 1988) Becke3–Perdew86 exchange-correlation func-

ITS-90 International Temperature (www.its-90.com)

Scale

of

1999

tional (Perdew, 1986; Becke, 1993)

(liq)

liquid

(cr) DFT

crystal density functional theory

Ln MI

lanthanide matrix isolation

DS DSC

relativistic Dirac–Slater calculation differential scanning calorimetry

MP2

second order Møller–Plesset perturbation theory (Møller and Plesset, 1934)

ECPD relativistic effective core potential of Dolg et al.

QC

quantum chemical computation

(1989) ECPS relativistic effective core potential of Stevens et al. (Stevens et al., 1992; Cundari and Stevens,

(sln) TZ

solution triple-zeta basis set

VDZ

valence double-zeta basis set

VTZ

valence triple-zeta basis set

ED

1993) electron diffraction

1. Introduction The lanthanide trihalides have been subject of studies for many decades. The main incentive has been the scientiﬁc interest in the physical and chemical properties of compounds of the trivalent lanthanide ions, which are unique in the period system as they regularly vary along

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

149

the series. This is due to the fact that the f electrons in the lanthanide ions are localised and do not actively participate in the chemical bonding. A similar effect occurs in the heavy actinide series for the elements beyond plutonium, which exhibit lanthanide-like properties. Because these heavy actinides are highly active materials, understanding of the lanthanide properties is the key to the prediction of the properties of the trivalent actinides, like americium and curium. The lanthanide halides also have important technological relevance. In the 1950s and 1960s some interest in the ﬂuorides originated from nuclear technology. The molten salt reactor project in the USA initiated many studies on the LnF3 compounds as these are formed in the (LiF-BeF2 -ThF4) fuel that was used. Separation of these ﬁssion products from the actinides during the pyrochemical reprocessing of the fuel was an important issue. A pyrochemical process was also developed for the reprocessing of the metal fuel for the fast reactor programme in the USA. This process is based on dissolution of the fuel in a high temperature molten chloride salt and selective transport to a metal cathode. In recent years, these technologies have found re-newed interest in the nuclear community, mainly in the frame of the actinide partitioning and transmutation programmes (Baetslé, 1999), for which the separation of the lanthanide ﬁssion products from the (trivalent) actinides is a key issue. Lanthanide bromides and iodides have found important applications in a completely different ﬁeld. They are added as additives in high-pressure discharge lamps in the lighting industry to improve the arc stability and the colour quality. The latter is due to the contribution of the multiline spectrum of the doped rare earths which are added to the salt mixture. Lanthanide trihalides of dysprosium, holmium, thullium, gadolinium and lutetium are used frequently for this purpose (Hilpert and Niemann, 1997). These high temperature processes can be modelled adequately by equilibrium thermodynamics. For such calculations reliable thermodynamic data are a priority. Although numerous studies of the thermodynamic properties of the lanthanide trihalides have been published in the past, the available information is still not complete. But because the properties change regularly within the lanthanide series, estimates can help to obtain the data that are lacking. In the present chapter the existing information is reviewed and emphasis is given to the understanding of the trends in order to establish a basis for the estimations. The cited literature is essentially from the period 1945–2002. The studies made before that period are considered to be less reliable as the separation technology to obtain the lanthanide elements in pure form was not sufﬁciently well developed before 1945 (Spedding and Daane, 1960).

2. Polymorphism 2.1. LnF3 Four crystallographic modiﬁcations have been reported for the lanthanide triﬂuorides (Greis and Haschke, 1982; Meyer and Wickleder, 2000). The triﬂuorides of La, Ce, Pr and Nd have a hexagonal/trigonal structure from room temperature up to the melting point. Greis and Cader (1985) reported that these compounds undergo a λ-type second order transition before melting, which was easier to detect when the samples were heated at low heating rates. As a result

150

R.J.M. KONINGS AND A. KOVÁCS

Fig. 1. The polymorphism in the lanthanide triﬂuorides.

the transition temperatures are not well deﬁned. Greis and Cader (1985) argued that at low temperatures a highly ordered superstructure exits (space group P 3c1) whereas the aniondisordered structure (space group P 63 cm) dominates at higher temperatures. The triﬂuorides of Sm to Lu have an orthorhombic structure (space group Pnma) at room temperature. Transitions from the orthorhombic to a hexagonal structure at elevated temperature have been reported for all compounds in the series Sm–Lu: the LaF3 type hexagonal structure for the triﬂuorides of Sm to Ho and the YF3 hexagonal structure for the triﬂuorides of Er to Lu. Stankus et al. (1999) concluded that the transition involves a deformation mechanism and may occur over a broad temperature range. Pastor and Robinson (1974) and Sobolev et al. (1976a, 1976b) discussed the variation in transition temperatures in view of hydroxide, oxygen and alkaline earth impurities and argued that the transitions in TbF3 , DyF3 and HoF3 do not occur and that the reported claims are due to impurities. The polymorphism as a function of atomic number is shown in ﬁg. 1, which is essentially identical to the ﬁgure of Greis and Haschke (1982) in an earlier chapter of this Handbook series. The reported transition and melting temperatures are summarised in table A.1 of Appendix A. As follows from the discussed above, there is quite some variation in the transition temperatures, but there is generally good agreement for the melting temperatures of the lanthanide triﬂuorides. The selected values (considering corrections to ITS-90) are summarised in table 1. Figure 1 shows that a minimum in the melting curve of the lanthanide triﬂuorides occurs at ErF3 : the melting point steadily decreases with increasing atomic number for the light hexagonal/trigonal and orthorhombic but slightly increases for the heavy hexagonal triﬂuorides. Since data for PmF3 are lacking, its melting point has been interpolated. 2.2. LnCl3 The lanthanide trichlorides of La to Eu have a hexagonal crystal structure (space group P 63 /m) at room temperature. For GdCl3 the hexagonal as well as the orthorhombic structures have been reported at room temperature. There is some uncertainty which of these is the

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

151

Table 1 The selected transition and melting temperatures for the lanthanide trihalides, in K F Ttrs La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

743 ± 3 973 ± 3 1347 ± 3

1388 ± 3 1325 ± 3 1267 ± 3 1230 ± 3

Cl Tfus 1766 ± 3 1703 ± 3 1670 ± 3 1649 ± 3 1605 ± 15 1571 ± 3 1549 ± 3 1501 ± 3 1446 ± 3 1426 ± 3 1416 ± 3 1413 ± 3 1431 ± 3 1435 ± 3 1455 ± 3

Ttrs

872 ± 10 783 ± 5 611 ± 5 820 ± 20

Br Tfus 1133 ± 5 1090 ± 2 1060 ± 2 1032 ± 2 994 ± 15 950 ± 5 894 ± 3 875 ± 2 855 ± 3 924 ± 3 993 ± 3 1049 ± 5 1095 ± 3 1138 ± 5 1198 ± 5

Ttrs

I Tfus 1060 ± 3 1005 ± 2 965 ± 3 955 ± 2 930 ± 15 913 ± 5 978 ± 10 1043 ± 5 1102 ± 3 1152 ± 3 1192 ± 3 1196 ± 5 1228 ± 3 decomp. 1298 ± 5

Ttrs

859 ± 3 900 ± 10 943 ± 10 1013 ± 5 1080 ± 5 1101 ± 5 1150 ± 15 1195 ± 15 1240 ± 15 1280 ± 15 1320 ± 15

Tfus 1045 ± 3 1033 ± 2 1011 ± 2 1059 ± 2 1090 ± 10 1123 ± 5 decomp. 1204 ± 3 1229 ± 3 1251 ± 3 1267 ± 5 1288 ± 3 1294 ± 5 decomp. 1323 ± 5

thermodynamically stable form. Because Sommers and Westrum Jr. (1977) were not able to transform the hexagonal form to the orthorhombic by annealing (367 K, 7 days) or cooling (liquid nitrogen, 7 h), they considered the hexagonal structure to be the thermodynamically stable form. This was conﬁrmed by Raman spectroscopic studies by Daniel et al. (1989). TbCl3 has an orthorhombic structure (space group Cmcm). The trichlorides of Dy to Lu have a monoclinic crystal structure (space group C2/m). The hexagonal structure of the trichlorides of La to Eu persists up to the melting point, whereas GdCl3 retains its hexagonal structure up to few degrees below to the melting point (Daniel et al., 1989). The high temperature behaviour of the orthorhomic and monoclinic lanthanide trichlorides is not so well known. The enthalpy increment studies for TbCl3 , DyCl3 and HoCl3 (Dworkin and Bredig, 1971) do not reveal any phase transformations up to the melting point (see below), but differential scanning calorimetric measurements of DyCl3 and ErCl3 revealed transitions at 611 K and 1025 K (Gaune-Escard et al., 1994), respectively, the nature of which was not explained. Büchel et al. (1995) claimed that in the case of ErCl3 the DTA peak is due to the reaction with the silica crucible used by Gaune-Escard et al. (1994). Morrison et al. (2000) studied the polymorphism of TbCl3 by Raman spectroscopy and Xray diffraction and demonstrated that a phase change occurs around 773 K and tentatively assigned it to a tetragonal structure (space group P 42 /mnm), in agreement with the work of Gunselius et al. (1988). The reported transition and melting temperatures are listed in table A.2 of Appendix A. There is general agreement between the studies and the selected values (considering corrections to ITS-90) are summarised in table 1. The polymorphism as a function of atomic number is shown in ﬁg. 2. The minimum in the melting curve of the lanthanide trichlorides occurs at TbCl3 where a change in structure of the LnCl3 occurs, as was the case for the triﬂuorides. Data for PmCl3 are lacking and its melting point has been interpolated in the LnCl3 series.

152

R.J.M. KONINGS AND A. KOVÁCS

Fig. 2. The polymorphism in the lanthanide trichlorides.

2.3. LnBr3 The tribromides of La, Ce and Pr have a hexagonal structure (space group P 63 /m), the tribromides of Nd, Pm, Sm and Eu have an orthorhombic structure (space group Cmcm), and the tribromides of Tb to Lu have a hexagonal/rhombohedral structure (space group R3). For GdBr3 several different crystal structures have been reported: hexagonal/rhombohedral, trigonal and monoclinic, the former being the thermodynamically stable phase. Phase transformations have not been reported for any of the rare earth tribromides, but only a few detailed studies of the high-temperature phase behaviour have been made. Brown et al. (1968) did not ﬁnd evidence for polymorphism in GdBr3 by X-ray diffraction; Dworkin and Bredig (1971) none for LaBr3 , CeBr3 , PrBr3 , NdBr3 , GdBr3 or HoBr3 by drop-calorimetric measurements; and Cordfunke et al. (Cordfunke and Blacquère, 1997; Cordfunke et al., 1999) none for NdBr3 and DyBr3 by differential scanning calorimetric measurements. The reported melting points for the tribromides are in good agreement as shown in table A.3 of Appendix A. The recommended melting points (considering corrections to ITS-90) are listed in table 1, and shown as a function of atomic number in ﬁg. 3. The minimum in the melting curve of the lanthanide tribromides occurs at SmBr3 or perhaps PmBr3 . Unlike the ﬂuoride, chloride and iodide series, no change in structure has been reported in the bromide series at this point. This observation may, however, be an indication that a high-temperature orthorhombic-hexagonal phase transformation occurs for EuBr3 and eventually for SmBr3 , and the stability ﬁelds in ﬁg. 3 have been drawn schematically to reﬂect this. Because of these uncertainties the melting point of PmBr3 is difﬁcult to estimate accurately. 2.4. LnI3 The triiodides of La to Nd have an orthorhombic structure (space group Ccmm), the triiodides of Sm to Lu have a hexagonal/rhombohedral structure (space group R3). High temperature transformations have been reported for the lanthanide triiodides from NdI3 to DyI3 . The orthorhombic NdI3 probably transforms into the rhombohedral structure (Dworkin and Bredig,

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

153

Fig. 3. The polymorphism in the lanthanide tribromides.

Fig. 4. The polymorphism in the lanthanide triiodides.

1971). The nature of the transformations in for the triiodides SmI3 to DyI3 is not deﬁned and it is unclear whether this transformation also occurs in HoI3 , ErI3, TmI3 and LuI3 as these compounds have hardly been studied. As the enthalpies of these transitions are small, it is most likely that they involve a rearrangement of the rhombohedral lattice. For the diagram in ﬁg. 4 we have linearly extrapolated the transition temperatures beyond DyI3 based on the straight line established by the LnI3 transformation temperatures for Ln = Nd, Sm, Gd, Tb, and Er. This ﬁgure is, however, of a speculative nature. The melting points of LaI3 to NdI3 have been studied by several authors and the results agree well and selected values (considering corrections to ITS-90) are given in table 1. For the heavy lanthanide triiodides only a limited number of studies has been made, but the reliability is good (see table A.4 of Appendix A). No experimental studies are known for PmI3 , EuI3 and YbI3 . The latter two compounds start to decompose below the melting point. The melting point of PmI3 has been interpolated in the LnI3 series.

154

R.J.M. KONINGS AND A. KOVÁCS

3. Low-temperature heat capacity and standard entropy of the solid trihalides 3.1. LnF3 The heat capacity of hexagonal/trigonal LaF3 , PrF3 and NdF3 and orthorhombic GdF3 , DyF3 , ErF3 and LuF3 was measured by Lyon et al. (1978, 1979a, 1979b) and Flotow and O’Hare (1981, 1984) using adiabatic low-temperature calorimetry in the 5 to 350 K range. The heat capacity of CeF3 was measured by King and Christensen (1959) from 51 to 298.15 K, and by Westrum Jr. and Beale Jr. (1961) from 5 to 300 K. The heat capacity curves of all these compounds show a smooth and continuous increase up to 350 K, indicating no transitions. The heat capacity of the trivalent lanthanide trihalides consists of a lattice component, arising mainly from the vibrations of the ions in the crystal, and an excess component (Westrum Jr. and Grønvold, 1962; Westrum Jr., 1970; Flotow and Tetenbaum, 1981; Westrum Jr., 1983): Cp = Clat + Cexs .

(1)

The excess contribution is due to the distribution of the valence electrons over the energy levels, and includes the splitting of the ground term by the crystalline electric ﬁeld (Stark effect) and is called the Schottky heat capacity or Schottky anomaly. It can be calculated from

Table 2 The crystal ﬁeld energy levels for the lanthanide triﬂuorides (Dieke et al., 1968; Morrison and Leavitt, 1982) compound LaF3 CeF3 PrF3 NdF3 PmF3 SmF3 EuF3

GdF3 TbF3 DyF3 HoF3 ErF3 TmF3 YbF3 LuF3

state 1S 0 2F 5/2 2F 7/2 3H 4 4I 9/2 4I 11/2 2F 7/2 6H 5/2 6H 7/2 7F 0 7F 1 7F 2 8F 7/2 7F 6 6H 15/2 5I 8 4F 15/2 3H 6 3F 7/2 1S 0

εi /cm−1 0 0, 151, 280 2160, 2240, 2635, 2845 0.0, 59.7, 69.4, 134.7, 202.4, 222.6, 290.4, 330.7, 500.1 0, 45, 136, 296, 500 1978, 2037, 2068, 2091, 2187, 2223 0.00, 44.5, 159.4 1003.4, 1047.0, 1100.6, 1187.0 0.00 313, 375, 415 946, 997, 1098 0 0, 42, 60, 125, 140, 169, 209, 212, 217, 232, 319, 353, 488 0, 42.3, 61.8, 110.9, 154.9, 210.7, 272.3, 468.5 0, 7.3. 18.7, 32.5, 54.1, 76.7, 103.5, 125.3, 149.4, 204.2, 211.1 0, 52.0, 64.3, 96.5, 113.7, 141.6, 181.0, 229.3 0, 67, 118, 156, 204, 235, 272, 274, 349, 354, 400, 418, 441 0, 78, 185, 401 0

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

155

the partitioning function Q, which is described by the Maxwell–Boltzmann distribution law: Qexs =

n

gi e−εi /RT ,

(2)

i=0

where εi is the energy and gi the degeneracy of level i, R is the universal gas constant and T is the absolute temperature. The excess heat capacity is then calculated from the equations: d 2 d(ln Q) T . Cexs = R (3) dT dT The electronic states of the lanthanide 3+ ions are characterised by (2J + 1)-fold degeneracy which is removed by the crystalline electric ﬁeld. For the ground state this results in a set of energy levels generally below 1000 cm−1 . These crystal-ﬁeld states have been identiﬁed for most of the lanthanide triﬂuorides, and are summarised in table 2. Examples of Cexs thus calculated are shown in ﬁg. 5 for PrF3 , NdF3 , DyF3 , and ErF3 . In LaF3 , GdF3 and LuF3 the excess contribution is zero which is due to the fact that these lanthanide ions have an empty, half-ﬁlled and completely ﬁlled f-shell, respectively. This is evident from a plot of the Cp values at 298.15 K as a function of the atomic number as shown in ﬁg. 6 which indicates that the values for these three compounds form a straight line, is spite of their different crystal structures. Flotow et al. resolved the lattice and excess contribution by assuming the heat capacity of LaF3 to represent the lattice component of the other hexagonal earth triﬂuorides (PrF3 , NdF3 ) and GdF3 and LuF3 that of the orthorhombic rare earth triﬂuorides. Flotow et al. obtained the values in between GdF3 and LuF3 by an interpolation using weighing factor f based on the molar volume: Clat = (1 − f )Clat (GdF3 ) + f Clat (LuF3 ).

Fig. 5. The excess heat capacity of PrF3 , NdF3 , DyF3 and ErF3 as calculated from the crystal ﬁeld energies.

(4)

156

R.J.M. KONINGS AND A. KOVÁCS Fig. 6. The variation of Cp (298.15 K) in the lanthanide triﬂuoride series (◦). The broken line connects the values for LaF3 , GdF3 and LuF3 for which Cexs is zero at 298.15 K. The solid circles show the values of Clat (298.15 K) obtained by subtracting Cexs (298.15 K) from the experimental values.

Fig. 7. The excess heat capacity of DyF3 ; curve shows the values calculated from the crystal ﬁeld energies, symbols are the values derived from the experimental data by subtracting Clat , as explained in the text.

The experimental excess heat capacity thus obtained as the difference between measured Cp and Clat can then be compared to the values calculated from the crystal ﬁeld levels. As an example, ﬁg. 7 shows the good agreement of the experimental and calculated excess heat capacity of DyF3 . The standard molar entropies at 298.15 K derived from the low-temperature heat capacity measurements are summarized in table 3. Similar to the heat capacity, the entropy can be described as the sum of the lattice and excess components (Konings, 2001, 2002): S = Slat + Sexs .

(5)

The excess entropy is then calculated from the following equation: Sexs = R ln Qexs .

(6)

Combining eqs. (2) and (6) gives: n −εi /RT . gi e Sexs = R ln(g0 ) + R ln

(7)

i=1

The ﬁrst term of eq. (7) represents the temperature independent contribution of the ground state, the second term the contribution of the excited energy levels. The lattice contribution in the lanthanide ﬂuorides is only known with sufﬁcient accuracy when the f shell of the metal ions is empty (4f0 ) or completely ﬁlled (4f14 ). In these cases Sexs is zero and the experimental entropy corresponds to Slat . Also in case the f-shell of the metal

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

157

Table 3 The entropies of the solid lanthanide(III) ﬂuorides and chlorides at 298.15 K, in J·K−1 ·mol−1 Experimentala

Calculated LaF3 CeF3 PrF3 NdF3 PmF3 SmF3 EuF3 GdF3 TbF3 DyF3 HoF3 ErF3 TmF3 YbF3 LuF3 LaCl3 CeCl3 PrCl3 NdCl3 PmCl3 SmCl3 EuCl3 GdCl3 TbCl3 DyCl3 HoCl3 ErCl3 TmCl3 YbCl3 LuCl3

Slat 105.84 104.97 104.10 103.23 102.37 101.50 100.63 99.76 98.90 98.03 97.16 96.29 95.42 94.55 93.69 137.57 136.71 136.28 135.85 135.42 134.99 134.56 134.13 133.70 155.15 154.72 154.29 153.86 153.43 153.00

Sexs 0.00 13.73 16.75 17.24 18.27 15.00 9.44 17.29 20.07 21.83 23.18 22.62 19.56 17.29 0.00 0.00 14.71 17.87 18.30 17.89 15.27 9.32 17.29 21.15 22.83 23.16 22.60 20.84 15.80 0.00

Stot 105.84 118.70 120.85 120.47 120.64 116.50 110.07 117.05 118.97 119.86 120.34 118.91 114.98 111.84 93.69 137.57 151.42 154.15 154.15 153.31 150.26 143.88 151.42 154.85 177.98 177.88 176.89 174.70 169.23 153.0

Sexp 106.98 ± 0.11 115.23 121.22 ± 0.12 120.79 ± 0.12 – – – 114.77 ± 0.22 – 118.07 ± 0.12 – 116.86 ± 0.12 – – 94.83 ± 0.09 137.57 – 153.30 153.43 – 150.12 144.06 151.42 – 175.4 177.1 175.1 173.5 169.3 153.0

References 1 2 3 4

5 6 6

5 7 7 7 8 8 8 9 10 11 12 13 9

a The uncertainty for the standard entropies derived from the calorimetric measurements has not been given in some cases.

References 1. Lyon et al. (1978) 2. Westrum Jr. and Beale Jr. (1961) 3. Lyon et al. (1979a) 4. Lyon et al. (1979b) 5. Flotow and O’Hare (1981)

6. Flotow and O’Hare (1984) 7. Sommers and Westrum Jr. (1976) 8. Sommers and Westrum Jr. (1977) 9. Tolmach et al. (1987) 10. Tolmach et al. (1990a)

11. Tolmach et al. (1990b) 12. Tolmach et al. (1990c) 13. Gorbunov et al. (1986)

ion is half ﬁlled (4f7 ), Slat can be derived easily from the experimental entropy since only a correction for the temperature independent term in eq. (7) needs to be made in the absence of a signiﬁcant crystal-ﬁeld splitting of the ground state. In ﬁg. 8 the experimental entropies for the lanthanide triﬂuorides are plotted as a function of the atomic number. The ﬁgure shows that Slat for LaF3 , GdF3 and LuF3 form approximately

158

R.J.M. KONINGS AND A. KOVÁCS Fig. 8. The variation of the Sexp (◦) and Slat (•) in the lanthanide triﬂuorides. The broken line shows Slat derived from the values for LaF3 , GdF3 and LuF3 , the solid line shows Sexs derived from the experimental data for the other conﬁgurations.

a straight line, as was the case for the heat capacities at 298.15 K. Slat for the other lanthanide compounds is then obtained by inter- or extrapolation of the data (which is a simpler, but essentially identical approximation as the weighing factors based on the molar volume, as indicated by eq. (4)). These numbers are listed in table 3. The excess contribution is calculated from eq. (7) using the crystal ﬁeld energies listed in table 2, which are mainly based on spectroscopic studies of the lanthanide ions in transparent host crystals. In case of PmF3 the spectroscopic data are missing, and Sexs is calculated from the degeneracy of the ground state of the lanthanide ion. This neglect of the crystal energy splitting leads to a small overestimation of Sexs at 298.15 K, which increases when the energy gap of the crystal-ﬁeld splitting becomes larger. For example, we obtain Sexs = 17.24 J·K−1 ·mol−1 at 298.15 K for NdF3 from the known crystal ﬁeld levels, whereas we obtain Sexs = R ln(10) = 19.14 J·K−1 ·mol−1 at 298.15 K from the approximation. The total entropy values thus obtained for CeF3 , PrF3 , NdF3 , DyF3 and ErF3 compare well with the experimental values by Flotow et al. and the difference Sexp − Stot is in the order of 1–2%. The recommended entropy values are the experimental values of Flotow et al., and the calculated values for those compounds for which no experimental data are available. An uncertainty of ±3.0 J·K−1 ·mol−1 has been assigned to the calculated values. 3.2. LnCl3 Heat capacity measurements in the 10 to 350 K temperature range have been reported by Sommers and Westrum Jr. (1976, 1977) for the hexagonal lanthanide trichlorides and Tolmach et al. for the monoclinic ones (Gorbunov et al., 1986; Tolmach et al., 1987, 1990a, 1990b, 1990c). No compound was measured in parallel by both groups but remarkable differences are observed between the results of the two groups. This is shown in ﬁg. 9 in which the heat capacity curves of GdCl3 measured by Sommers and Westrum and LuCl3 by Tolmach et al. are plotted. It can be seen that the heat capacity curve of LuCl3 is signiﬁcantly higher than that of GdCl3 up to about 150 K above which the heat capacity curve approach each other. This is signiﬁcantly different from the situation for the triﬂuorides where the curves of LaF3 , GdF3 and LuF3 have the same shape and the heat capacity slightly decreases with increasing atomic number. The differences in the entropy values derived for the two groups of compounds are also signiﬁcant: the lattice values at 298.15 K derived from the work of Tolmach et al. are about 20 J·K−1 ·mol−1 higher than the extrapolation of results for the hexagonal compounds, as

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

159

Fig. 9. The heat capacity of GdCl3 () and LuCl3 ().

Fig. 10. The variation of Sexp (◦, hexagonal; , monoclinic) and Slat (•) in the lanthanide trichloride series at 298.15 K; the broken line shows the lattice contribution (see text).

Fig. 11. The molar volumes in the LnF3 (◦) and LnCl3 series () at 298.15 K.

shown in ﬁg. 10. This suggests a distinct difference between entropies of hexagonal and monoclinic crystallographic modiﬁcations. This difference is also evident in the molar volumes (ﬁg. 11): Vm of the lanthanide triﬂuorides, calculated from the lattice constants, decreases lin-

160

R.J.M. KONINGS AND A. KOVÁCS

Table 4 The corrected standard entropy values at 298.15 K for the monoclinic lanthanide(III) chlorides (in J·K−1 ·mol−1 ) as derived from the work of Tolmach et al. (Tolmach et al., 1987, 1990a, 1990b, 1990c; Gorbunov et al., 1986); Tmin is lower temperature limit of the measurements DyCl3 HoCl3 ErCl3 TmCl3 YbCl3

Tmin 0 6.61 9.86 15.34 0

Sexp (298.15 K − Tmin ) 169.6 170.1 168.1 166.5 163.5

Slat (Tmin ) 0.00 0.25 1.25 3.35 0.00

Sexs (Tmin ) 5.76 6.74 5.76 3.68 5.76

S ◦ (298.15 K) 175.4 177.1 175.1 173.5 169.3

Table 5 The crystal ﬁeld energy levels for the lanthanide trichlorides (Morrison and Leavitt, 1982; Carnall, 1982) compound LaCl3 CeCl3 PrCl3 NdCl3 PmCl3 SmCl3 EuCl3

GdCl3 TbCl3 DyCl3 HoCl3 ErCl3 TmCl3 YbCl3 LuCl3

state 1S 0 2F 5/2 2F 5/2 3H 4 4I 9/2 4I 11/2 2F 7/2 6H 5/2 6H 7/2 7F 0 7F 1 7F 2 8F 7/2 7F 6 6H 15/2 5I 8 4F 15/2 3H 6 3F 7/2 1S 0

εi /cm−1 0 0, 37.5, 110 2166, 2208.6, 2282.6, 2399.5 0, 33.1, 96.4, 130.2, 137.0, 199.1 0, 115.4, 123.2, 244.4, 249.4 1973.85, 2012.58, 2026.90, 2044.19, 2051.60, 2058.90 0, 66.6, 84.5, 110.1, 127.0, 240.0 0, 40.7, 66.1 992.8, 1051.2, 1104.7, 1172.6 0 355,05, 405.27 1022.54, 1027.52, 1084.33 0 0, 56.8, 90.6, 97.2, 99.3, 104.6, 112.8, 118.0 0, 9.82, 9.97, 15.65, 40.8, 80.5, 121.7, 140.5 0, 12.5, 43.8, 66.4, 89.9, 104.1, 118.4, 154.2, 155.4, 203.7, 212.8 0, 37.9, 64.3, 96.5, 113.7, 141.6, 181.0, 229.43 0, 29, 92, 121, 127, 181, 193, 195, 207 0, 50, 185, 401 0

early along the series due to the lanthanide contraction with almost no difference between the two crystal structures, whereas Vm of the lanthanide trichlorides shows a distinct difference between the hexagonal and the monoclinic compounds. The data shown in ﬁg. 10 are not the values reported by Gorbunov et al. (1986) and Tolmach et al. (1987, 1990a, 1990b, 1990c), because they did not extrapolate their measurements to 0 K in all cases. To derive S ◦ (298.15 K) we have assumed that the heat capacity of LuCl3 represents the lattice component, and Slat at the lower temperature limit is derived from the results for this compound. The excess contribution at this temperature is calculated from the crystal ﬁeld energies (see table 5) derived from spectroscopic studies of the ions in transparent host crystals (Dieke et al., 1968; Morrison and Leavitt, 1982;

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

161

Carnall, 1982). The ‘experimental’ standard entropy values thus obtained for the monoclinic lanthanide trichlorides are listed in table 4. The entropies for those compounds for which no experimental data have been reported (CeCl3 , PmCl3 , TbCl3 ) are calculated according to the method outlined for the triﬂuorides. The lattice component has been derived from linear interpolation between LaCl3 and GdCl3 for the hexagonal compounds and a parallel relation ﬁtted to the LuCl3 value for the monoclinic compounds. The excess entropies have been calculated from the energy levels of the Ln3+ ions. The calculated values for the standard entropy at 298.15 K (Stot ) are in good agreement with the calculated values obtained from the sum of the lattice and excess contribution at 298.15 K, as shown in table 3. Because there is only one ‘reference’ point for the lattice contribution in the monoclinic series (LuCl3 ), the trend along this series is assumed to have the same slope as the hexagonal trichlorides. 3.3. LnBr3 and LnI3 Only a few low-temperature heat capacity measurements have been reported for the lanthanide tribromides and triiodides. Deline et al. (1975) measured the low-temperature heat capacity of EuBr3 , Gavrichev et al. (1992) of LuI3. These data are insufﬁcient to derive the lattice component as was done for the triﬂuorides and the trichlorides. In addition, few data on the crystal ﬁeld levels for the bromides and iodides are available (Morrison and Leavitt, 1982). A number of assumptions thus had to be made. Figure 12 shows that the trends in the molar volume of the LnBr3 and LnI3 series indicate two groups, as is the case for the trichlorides. We therefore conclude that the entropies of the two groups must be derived separately. The lattice entropies of the tribromides in the La–Eu series are obtained by subtracting Sexs from the measurements for EuBr3 and these values are used to approximate Slat , assuming that this quantity will vary regularly through the orthorhombic and hexagonal series. An estimated slope for the relation of Slat versus atomic number dependence was used. The same was done for rhombohedral triiodides using the experimental value for LuI3 . The lattice entropy of the rhombohedral tribromides and the orthorhombic triiodides have been derived by an extrapolation of the experimental values for the lanthanum (including the value for LaBr3 obtained indirectly from the experimental value of EuBr3 ) and lutetium trihalides, as shown in ﬁg. 13. The entropies of these compounds correlate perfectly with the logarithm of the molecular weight of the halide ion. The crystal ﬁeld levels in the tribromides and triiodides are assumed to be the same as in the trichlorides, which can be justiﬁed by the experimental data for PrBr3 ,

Fig. 12. The molar volumes in the LnBr3 () and LnI3 series () at 298.15 K.

162

R.J.M. KONINGS AND A. KOVÁCS

Fig. 13. The standard molar entropy as a function of the logarithm of the molecular weight of the halide atom ln(M); LaX 3 (◦), LuX 3 () and EuX 3 (); estimated values are indicated by and .

NdBr3 and ErBr3 doped in LaBr3 as given by Morrison and Leavitt (1982). The entropy data thus obtained are summarised in table 6.

4. High-temperature heat capacity of the solid trihalides 4.1. LnF3 Enthalpy increment measurements to derive the high-temperature heat capacity have been reported for all lanthanide triﬂuorides except PmF3 , as summarised in table 7. The results of the various authors are compared using the reduced enthalpy increment function: ◦ H (T ) − H ◦ (298.15 K) /(T − 298.15). (8) Figure 14 shows a plot of this function for LaF3 . It can be seen that the data for the enthalpy increment by Spedding and Henderson (1971) and Lyon et al. (1978) are in good

Fig. 14. The reduced enthalpy increment of LaF3 (in J·K−1 ·mol−1 ); ◦, Henderson (1970); Lyon et al. (1978); •, value at 298.15 K derived from the low-temperature heat capacity measurements of Lyon et al. (1978).

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

163

Table 6 The entropies of the solid lanthanide(III) bromides and iodides at 298.15 K, in J·K−1 ·mol−1 Experimentala

Calculated LaBr3 CeBr3 PrBr3 NdBr3 PmBr3 SmBr3 EuBr3 GdBr3 TbBr3 DyBr3 HoBr3 ErBr3 TmBr3 YbBr3 LuBr3

Slat 177.1 176.5 175.9 175.3 174.7 174.1 173.5 191.7 191.1 190.5 189.9 189.6 189.3 189.0 188.7

Sexs 0.00 14.71 17.87 18.30 17.89 15.27 9.32 17.29 21.15 22.83 23.16 22.60 20.84 15.80 0.00

Stot 177.1 191.2 193.8 193.6 192.6 189.4 182.8 209.0 212.3 213.4 213.1 212.2 210.2 204.8 188.7

Sexp – – – – – – 182.8 – – – – – – – –

LaI3 CeI3 PrI3 NdI3 PmI3 SmI3 EuI3 GdI3 TbI3 DyI3 HoI3 ErI3 TmI3 YbI3 LuI3

196.3 195.7 195.1 194.5 212.7 212.1 212.5 210.9 210.3 209.7 209.1 208.5 207.9 207.3 206.7

0.00 14.71 17.87 18.30 17.89 15.27 9.32 17.29 21.15 22.83 23.16 22.60 20.84 15.80 0.00

196.3 210.4 213.0 212.8 230.6 227.4 220.8 228.2 231.5 232.5 232.3 231.1 228.7 223.1 206.7

– – – – – – – – – – – – – – 206.7

References

1

2

a The uncertainty for the standard entropies derived from the calorimetric measurements has not been given in some cases.

References 1. Deline et al. (1975)

2. Gavrichev et al. (1992)

agreement, with the exception of the lowest data point of the former authors. The hightemperature results also reasonably ﬁt the low-temperature results by Lyon et al. (1978). The combined results have been ﬁtted to a polynomial equation, applying as boundary conditions {H ◦ (T ) − H ◦ (298.15 K)} = 0 at 298.15 K and Cp (298.15 K) = 90.29 J·K−1 ·mol−1 , as followed from the low-temperature measurements. The coefﬁcients of the polynomial are given in table 8. The data for the other triﬂuorides have been evaluated in a similar way, and the results are also listed in table 8. The values for Cp (298.15 K) of those compounds for which no

164

R.J.M. KONINGS AND A. KOVÁCS Table 7 Summary of the enthalpy increment measurements for the lanthanide triﬂuorides

compound LaF3 CeF3

PrF3 NdF3 SmF3 EuF3 GdF3

TbF3 DyF3 HoF3 ErF3 TmF3 YbF3 LuF3

T /K 390–1831 425–1477 398–1799 575–1373 400–1899 390–1831 727–1243 390–1831 727–1324 400–1887 400–1252 390–1831 576–1249 400–1803 400–1793 577–1173 400–1744 390–1831 432–1588 400–1841 400–1794 577–1175 400–1731 390–1831

number of data points 33 23 19 9 20 30 6 31 9 23 ? 27 8 ? ? 7 ? 27 63 21 ? 7 ? 30

References 1 2 3 4 5 1 4 1 4 5 5 1 4 5 5 4 5 1 6 5 5 4 5 1

References 1. Spedding and Henderson (1971) 2. Lyon et al. (1978)

3. King and Christensen (1959) 4. Charlu et al. (1970)

5. Spedding et al. (1974) 6. Lyapunov et al. (2000)

Fig. 15. The reduced enthalpy increment of PrF3 (in J·K−1 ·mol−1 ); ◦, Henderson (1970); Charlu et al. (1970); •, value at 298.15 K derived from the low-temperature heat capacity measurements of Lyon et al. (1979a).

low-temperature measurements have been reported are calculated from the sum of the lattice and excess contributions (eq. (1)). For most compounds there is good agreement between the various data sets, although the results of Henderson (1970), Spedding and Henderson (1971), that were reported as poly-

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

165

Table 8 Recommended high temperature heat capacity functions for the solid lanthanide triﬂuorides compound

Cp (298.15 K)

LaF3 CeF3 PrF3 NdF3 PmF3 SmF3

/kJ·mol−1 90.29 ± 0.09 93.47 ± 0.09 92.65 ± 0.09 92.42 ± 0.09 92.0 91.7

EuF3 GdF3 TbF3 DyF3 HoF3 ErF3 TmF3 YbF3 LuF3

hex orth hex orth hex orth

orth hex orth hex orth hex orth hex

97.9 88.39 ± 0.09 90.5 88.94 ± 0.09 88.6 90.07 ± 0.09 90.8 89.4 87.07 ± 0.09

Cp ◦ (T )/J · K−1 ·mol−1 = a + bT + cT 2 + dT 3 + eT −2

Tmax

trs H ◦

e × 10−6 −2.17138 −0.72087 −2.65559 −1.10117

/K 1766 1703 1670 1649

/kJ·mol−1

a 122.1188 103.2577 130.5994 103.3867

b × 103 −22.4674 −12.9896 −32.5026 1.66688

169.0564 −7.6809 297.1925 −370.3989 117.4275 150.6658 102.3403 6.0945 130.834 97.5769 19.8845 91.2338 28.2118 131.7639 −65.0032 121.3374 −30.3149 135.0177 115.6209 −17.1827 97.8638 103.7012 9.2366 119.5369 89.0368 19.2857 121.7126

c × 106 d × 109 −16.3094 28.1746 24.6881 18.1689 10.3935

−4.84076

189.2022

−3.1553 44.2500 22.7317 12.9143

743 1571 −1.73589 973 1549 −1.40162 1347 1501 −1.15610 1446 −0.926687 1426 −2.46383 1416 −2.15564 1388 1413 −1.85306 1325 1431 −1.51608 1267 1435 −0.68598 1230 1455

1.784 8.714 6.029

29.47 30.28 24.46 25.07

nomial equations only, tend to deviate at low temperatures in several of their measurements. This is evident in their tables which show a minimum in Cp around 500–600 K in those cases (e.g., ﬁg. 15). It is very likely caused by small errors which are ampliﬁed at low temperatures by the non-constrained ﬁtting procedure they used. In these cases the lowest temperature results have been omitted from our polynomial ﬁtting. Only for GdF3 and HoF3 the reported data are discordant. The results of Charlu et al. (1970), Spedding and Henderson (1971) and Spedding et al. (1974) for GdF3 are signiﬁcantly different. Since only the latter results agree well with the low-temperature heat capacity, they have been selected here. For HoF3 the situation is less clear. The results of Spedding and Henderson (1971) and Lyapunov et al. (2000) agree reasonably at low temperature, but the difference systematically increases with increasing temperature. The reason for this is unclear. We have preferred the results of Spedding and Henderson (1971) as their measurements on the other lanthanide triﬂuorides have proved to be highly reliable. In analogy with the approach that has been described in the section on the low-temperature heat capacity, the high-temperature heat capacity of the LnX 3 compounds can be described as the sum of the lattice and excess contributions (eq. (1)). However, whereas at low temperature the lattice heat capacity mainly arises from harmonic vibrations, at high temperatures the effects of anharmonicity of the vibrations, of thermal dilation of the lattice and of thermally

166

R.J.M. KONINGS AND A. KOVÁCS

induced vacancies in the lattice heat capacity have to be taken into account: Clat = Char + Canh + Cdil + Cvac .

(9)

According to theory, the molar harmonic contribution approaches the limit of 3R per atom, which corresponds to 12R for MX 3 compounds. Figure 14 shows that the heat capacity of LaF3 reaches this value around 900–1000 K but then increases strongly above 1100 K, an effect that is not seen very evident in any other lanthanide triﬂuoride (e.g., PrF3 in ﬁg. 15). Lyon et al. (1978) attributed this effect to the contribution of Cvac , and suggested that this contribution can amount to about 60 J·K−1 ·mol−1 near the melting point. An alternative/additional and more likely explanation can be found in the observations of Greis and Cader (1985) that the hexagonal/trigonal lanthanide triﬂuorides undergo a λ-type second order transition before melting, whose effect is strongest for LaF3 and becomes much weaker going from CeF3 to EuF3 . 4.2. LnCl3 The high-temperature heat capacity data for the lanthanide trichlorides are limited. Walden and Smith (1961) measured the enthalpy increment of CeCl3 , and Dworkin and Bredig (1971) determined the enthalpy increments of GdCl3 , TbCl3 , DyCl3 , and HoCl3 by drop calorimetry. Gaune-Escard et al. (Gaune-Escard et al., 1996; Rycerz and Gaune-Escard, 2002a, 2002b) measured the heat capacity of a selected number of compounds by differential scanning calorimetry (DSC). Only in a some cases (CeCl3 , GdCl3 , DyCl3 ) a comparison can be made between these studies and the agreement with the low-temperature heat capacity data checked. In ﬁg. 16 the results for GdCl3 are compared in a plot of the reduced enthalpy increment, which shows that the low-temperature data of Sommers and Westrum Jr. (1976) and the hightemperature data of Dworkin and Bredig (1971) are in excellent agreement. Also the results of Gaune-Escard et al. (1996) agree well, although they indicate a somewhat different slope of the curve. Figure 17 compares the results for LaCl3 of Gaune-Escard et al. (1996) again with the low-temperature data of Sommers and Westrum Jr. (1977), but also with the DSC data by Reuter and Seifert (1994). For this compound the results of Gaune-Escard et al. (1996) are signiﬁcantly lower than those of the other two studies, which agree very well.

Fig. 16. The reduced enthalpy increment of GdCl3 (in J·K−1 ·mol−1 ); •, Sommers and Westrum Jr. (1977); ◦, Dworkin and Bredig (1971); broken line, Gaune-Escard et al. (1996).

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

167

Fig. 17. The reduced enthalpy increment of LaCl3 (in J·K−1 ·mol−1 ); •, Sommers and Westrum Jr. (1976); ◦, Dworkin and Bredig (1963a); broken line (1), Gaune-Escard et al. (1996); broken line (2), Reuter and Seifert (1994).

Fig. 18. The excess heat capacity in LnCl3 compounds; •, CeCl3 ; ◦, PrCl3 ; , NdCl3 ; , PmCl3 ; , SmCl3 , , EuCl3 .

It is important to note that the curves for LaCl3 and GdCl3 , both of which do not have an electronic excess term due to the stable f0 and f7 electron conﬁgurations, are almost identical below 1000 K. This indicates that the lattice heat capacities in the hexagonal LnCl3 compounds between these compounds hardly vary. We thus can obtain the high-temperature heat capacity by adding Cexs to the lattice curve of LaCl3 or GdCl3 . Cexs is calculated from the known energy levels for these compounds, where not only the ground state energy levels but also the excited states are taken into account. The latter values are not shown in table 2, but can be found in the review by Morrison and Leavitt (1982). Figure 18 shows the variation of Cexs with temperature for the compounds CeCl3 to EuCl3 . Figure 19 shows that the heat capacity of CeCl3 thus obtained is in good agreement with the results of the enthalpy increment measurements by Walden and Smith (1961), whereas the heat capacity data reported by Gaune-Escard et al. (1996) are signiﬁcantly lower. Similarly, ﬁg. 20 shows that the calculated heat capacity of PrCl3 is in much better agreement with the low-temperature data than the experimental results of Gaune-Escard et al. (1996). For the monoclinic lanthanide trichlorides for which no experimental data are available we have estimated the lattice heat capacity by subtracting Cexs from the values of DyCl3 . The recommended heat capacity equations for the lanthanide trichlorides are listed in table 9.

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R.J.M. KONINGS AND A. KOVÁCS

Fig. 19. The reduced enthalpy increment of CeCl3 (in J·K−1 ·mol−1 ); , Walden and Smith (1961); •, estimated Cp (298.15 K); broken line, Gaune-Escard et al. (1996); solid line, calculated from Clat and Cexs .

Fig. 20. The reduced enthalpy increment of PrCl3 (in J·K−1 ·mol−1 ); •, Sommers and Westrum Jr. (1976); ◦, Dworkin and Bredig (1963a); broken line, Gaune-Escard et al. (1996); solid line, calculated from Clat and Cexs .

4.3. LnBr3 and LnI3 Dworkin and Bredig (1971) measured the enthalpy increments of the lanthanide tribromides CeBr3 , NdBr3 , GdBr3 and HoBr3 and triiodides LaI3 , NdI3 , GdI3 and TbI3 by dropcalorimetry. The heat capacity of LaBr3 was measured by Rycerz and Gaune-Escard (1999a), that of TmI3 by Gardner and Preston (1991) using differential scanning calorimetry. Lowtemperature data have not been reported for these compounds. As mentioned above, such data are only available for EuBr3 and LuI3 . We have ﬁtted the experimental enthalpy data to polynomial equations in the usual way, using estimated Cp (298.15 K) values as constraint. The latter were deduced from the low-temperature measurements by assuming a slight change in the lattice component along the series, as was observed for the triﬂuorides and trichlorides. This approach was preferred to a non-constrained ﬁtting procedure as this normally results in too high Cp (298.15 K) values. For example, the unconstrained ﬁt of CeBr3 results in Cp (298.15 K) = 105.1 J·K−1 ·mol−1 , whereas the estimated value is 101.9 J·K−1 ·mol−1 . The heat capacities for the other compounds were derived using the estimation procedure described for the trichlorides, i.e., from the lattice and excess contributions. The former was derived from the enthalpy measurements, the latter from the crystal ﬁeld energies. As the crystal energies of the tribromides and triiodides are poorly known, we have used the values for the trichlorides to approximate Cexs . The results thus obtained are listed in tables 10 and 11. The calculated data for TmI3 agree within 2% with the DSC results of Gardner and Preston (1991).

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

169

Table 9 High temperature heat capacity functions for the solid lanthanide trichlorides compound

Cp (298.15 K)

LaCl3 CeCl3 PrCl3 NdCl3 PmCl3 SmCl3 EuCl3 GdCl3 TbCl3

/J·K−1 ·mol−1 98.03 98.6 98.95 99.24 99.6 99.54 106.98 97.78 97.8

DyCl3 HoCl3 ErCl3 TmCl3 YbCl3 LuCl3

orth ?

100.5 101.9 99.78 100.0 101.4 96.62

Cp ◦ (T )/J·K−1 ·mol−1 = a + bT + cT 2 + dT 3 + eT −2

Tmax

trs H ◦

e × 10−6 0.68452 −0.27153 0.13465 0.04021

/K 1133 1090 1060 1032

/kJ·mol−1

0.56135 −0.26362 −0.03475

950 894 875 783 855 924 993 1049 1095 1138 1198

a 74.9288 90.9772 85.6511 87.2834

b × 103 51.6544 35.8123 39.5240 38.5855

95.3748 100.9736 88.7959 86.2920 123.930 104.5279 100.3820 101.4247 102.0423 104.8985 98.3259

33.4442 30.0922 31.4441 38.5982 −27.0190 5.0913 −16.3266 −17.9564 −23.8396 −17.9501

c × 106

d × 109

45.3111 36.2574 37.2518 40.6023 41.0146

18.68

Table 10 High temperature heat capacity functions for the solid lanthanide tribromides compound

Cp (298.15 K) /J·K−1 ·mol−1

LaBr3 CeBr3 PrBr3 NdBr3 PmBr3 SmBr3 EuBr3 GdBr3 TbBr3 DyBr3 HoBr3 ErBr3 TmBr3 YbBr3 LuBr3

101.6 101.9 102.3 103.1 103.0 103.1 110.62 ± 0.11 100.2 100.5 100.4 100.7 100.7 100.7 101.8 99.5

Cp ◦ (T )/J · K−1 ·mol−1 = a + bT + cT 2 + dT 3 + eT −2

Tmax

trs H ◦

e × 10−6

/K 1061 1005 965 955

/kJ·mol−1

913 978 1043 1102 1152 1192 1196 1228 1250a 1298

b × 103

c × 106

d × 109

a 97.4736 89.7173 93.6869 81.7525

17.9256 31.6041 26.6878 42.7393

−0.10828 0.24534 −0.05833 0.76491

103.2523 100.8207 93.8256 90.1490 92.3542 95.5581 94.3588 94.4929 96.5726 95.8694

20.7015 18.5433 14.2533 22.3082 16.8413 15.5998 13.7789 13.6251 11.6884 12.1770

−0.56223 0.37963 0.18888 0.32889 0.26887 0.04363 0.19850 0.19066 0.15489

a Decomposes before melting.

5. Enthalpy of formation of the solid trihalides 5.1. LnF3 Three different methods have been used to determine the enthalpies of formation of the lanthanide triﬂuorides: ﬂuorine combustion calorimetry, precipitation calorimetry and galvanic

170

R.J.M. KONINGS AND A. KOVÁCS Table 11 High temperature heat capacity functions for the solid lanthanide triiodides

compound

Cp (298.15 K)

Cp ◦ (T )/J·K−1 ·mol−1 = a + bT + cT 2 + dT 3 + eT −2

Tmax

trs H ◦

/J·K−1 ·mol−1 102.5 102.9 103.3 104.1

a b × 103 90.1970 27.5096 86.8928 35.1439 87.7509 34.7680 103.6598 −19.9550 120.450

e × 10−6 0.36456 0.49150 0.46074 0.15179

/K 1045 1033 1011 859 1059

/kJ·mol−1

LaI3 CeI3 PrI3 NdI3

16.8259 14.0032 13.1558

−0.16808 0.12116 0.17434

27.8840

0.41585

14.3586 12.2577 11.7695 11.4701 9.6833 13.5944

0.19028 0.16244 0.15597 0.15200 0.12832 0.17526

1123 1100a 1013 1204 1080 1229 1251 1267 1288 1294 1300a 1323

PmI3 SmI3 EuI3 GdI3 TbI3 DyI3 HoI3 ErI3 TmI3 YbI3 LuI3

orth hex?

hex hex? hex hex?

104.5 104.1 111.6 102.0 102.3 102.3 102.6 102.7 102.8 103.9 101.7 ± 0.3

100.9741 106.0620 96.1164 128.189 89.3082 124.334 95.8785 97.1180 97.4364 97.6703 99.5694 95.6752

c × 106

52.6734

d × 109

13.53

0.493 1.15

a Decomposes before melting.

cell studies. Combustion calorimetry is the most reliable of these three, though it is very sensitive to impurities in the starting metals. It has been applied for most of the lanthanide triﬂuorides and the results originate essentially from two laboratories, Argonne National Laboratory (ANL) in the USA and Kyoto University in Japan. Unfortunately the agreement between these two laboratories is variable for those cases where a comparison of the results can be made. For GdF3 and HoF3 the results agree very well, but for ErF3 they differ by ∼ 25 kJ·mol−1 , and for NdF3 by ∼ 19 kJ·mol−1 , which is well beyond the possible contribution of impurities. The precipitation measurements of the equilibrium: Ln3+ (aq) + 3F− (aq) = LnF3 (cr) are generally hindered by insufﬁcient knowledge of the precipitated phase, which can be amorphous instead of crystalline. The EMF measurements are in principle very accurate but unwanted electrode reactions may affect the results. Tables B.1 to B.14 of Appendix B summarise the data collected and reviewed for the lanthanide ﬂuorides and show that the agreement between the three techniques is indeed poor. Several methods have been proposed to check and correlate the data for the LnF3 compounds. A semi-empirical method was proposed by Kim and Johnson (1981) who used the Born–Landé equation to estimate the lattice energy Ulat : Ulat = NA Z1 Z2 e2 A(1 − 1/n)/r0 ,

(10)

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

171

Fig. 21. The enthalpy of formation of the lanthanide triﬂuorides as a function of the atomic number. ◦ and indicate the experimental results from ﬂuorine combustion studies at ANL and Kyoto University, respectively; the broken curve shows the estimated values using the Born–Landé equation (Kim and Johnson, 1981); the solid curve shows the values estimated values in this study (•).

where NA is the Avogadro’s constant, Z1 and Z2 are the oxidation numbers of the ions, e is the charge of a proton, A is the Madelung constant, n is the Born exponent and r0 is the characteristic distance of the lattice. The values that were thus obtained agree well with those derived from a Born–Haber cycle using the experimentally determined f H ◦ (298.15 K) values. Thus the calculated Ulat values could be used to obtain the enthalpies of formation of those triﬂuorides for which no or no reliable data are available. They are compared to the experimental ﬂuorine combustion results in ﬁg. 21, which shows good agreement for the ANL results, but not for the majority of the results of the Kyoto University. The trend of the f H ◦ along the LnF3 shows little variation, with the exception of the values for EuF3 and YbF3 which are signiﬁcantly less negative. This can be understood by looking at the Born–Haber cycle for the LnX 3 compounds (ﬁg. 22). Because Eu and Yb are divalent elements whereas the others are trivalent, the ionisation step to form Ln3+ in the cycle is different for these two elements as the stable 4f7 and 4f14 conﬁgurations have to be broken up to form the 4f6 and 4f13 conﬁgurations (Gschneidner Jr., 1969). To eliminate this effect, Morss (1976) and Fuger et al. (1983) proposed to use the quantity

f H ◦ (LnX3 , cr, 298.15 K) − f H ◦ Ln3+ , aq, 298.15 K (11) to analyse the data for lanthanide compounds. They correlated this quantity with molar volume or ionic radius for the lanthanide and actinide trihalides. The relation with ionic radius is shown in ﬁg. 23, using the enthalpies of formation of the aqueous ions from Cordfunke and Konings (2001a). It can be seen that the ANL results indicate two straight lines for the two crystallographic modiﬁcations (as is the case for the lanthanide trichlorides, tribromides and triiodides). The results of the Kyoto University (not shown in this ﬁgure) are widely scattered, whereas the values calculated by Kim and Johnson (1981) from the Born–Landé equation approximately agree with the trend, with strongly deviating values for SmF3 , DyF3 and YbF3 . On the basis of these considerations we have based our recommended values (table 12) on the ﬂuorine combustion data from ANL only, and have estimated the values for those compounds for which no data are available by inter- and extrapolation of the linear trends shown in ﬁg. 23.

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R.J.M. KONINGS AND A. KOVÁCS

Fig. 22. The Born–Haber cycle for the lanthanide trihalides.

Fig. 23. The quantity f H ◦ (LnF3 , cr) − f H (Ln3+ , aq) as a function of the ionic radius (coordination number 6); ⊕, hexagonal and ◦ orthorhombic structure.

5.2. LnCl3 , LnBr3 and LnI3 A careful review of all experimental data for the lanthanide chlorides, bromides and iodides, mainly made by solution calorimetry, has been made by Cordfunke and Konings (2001b) recently, who evaluated data from the literature between 1940 and 2000. The tables of this work are reproduced in Appendix B, corrected for some small errors. The present section summarises the justiﬁcation of the selected values. Two thermochemical reaction schemes are generally used to derive the enthalpies of formation of these compounds. The ﬁrst is based on the dissolution of the lanthanide metal as well

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

173

Table 12 Selected enthalpies of formation of the solid lanthanide trihalides, in kJ·mol−1 La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

F −1699.5 ± 2.0 −1689.2 ± 5.0 −1689.1 ± 2.6 −1679.4 ± 1.9 −1675 ± 20 −1700.7 ± 5.0 −1611.5 ± 5.0 −1699.3 ± 2.3 −1695.9 ± 5.0 −1692.0 ± 1.9 −1697.8 ± 2.3 −1693.6 ± 1.9 −1693.7 ± 5.0 −1655.1 ± 5.0 −1679.9 ± 5.0

Cl −1071.6 ± 1.5 −1059.7 ± 1.5 −1058.6 ± 1.5 −1040.9 ± 1.0 −1030 ± 10 −1025.3 ± 2.0 −935.4 ± 3.0 −1018.2 ± 1.5 −1010.6 ± 3.0 −993.1 ± 3.0 −997.7 ± 2.5 −994.4 ± 2.0 −996.3 ± 2.5 −959.5 ± 3.0 −987.1 ± 2.5

Br −904.4 ± 1.5 −891.2 ± 1.5 −890.5 ± 4.0 −864.0 ± 3.0 −858 ± 10 −853.4 ± 3.0 −759 ± 10 −838.2 ± 2.0 −843.5 ± 3.0 −834.3 ± 2.5 −842.1 ± 3.0 −837.1 ± 3.0 −832 ± 10 −791.9 ± 2.0 −814 ± 10

I −673.9 ± 2.0 −666.8 ± 3.0 −664.7 ± 5.0 −639.2 ± 4.0 −634 ± 10 −621.5 ± 4.0 −538 ± 10 −624.1 ± 3.0 −623.8 ± 3.0 −616.7 ± 3.0 −622.9 ± 3.0 −619.0 ± 3.0 −619.7 ± 3.5 −578 ± 10 −605.1 ± 2.2

as the lanthanide trihalide in hydrogen-saturated hydrochloric acid HCl(sln). The reaction scheme for the lanthanide trichlorides looks as follows: Ln(cr) + 3HCl(sln) = LnCl3 (sln) + 32 H2 (g) LnCl3 (cr) + 3HCl(sln) = LnCl3 (sln) + 3HCl(sln) 3 3 2 H2 (g) + 2 Cl2 (g) = 3HCl(sln) Ln(cr) + 32 Cl2 (g) = LnCl3 (cr)

r H 1◦ r H 2◦ r H 3◦ r H 4◦

The standard molar enthalpy of formation of LnCl3 (cr) equals to r H 4◦ , and can be calculated as: f H ◦ (LnCl3 , cr, 298.15 K) = r H 1◦ − r H 2◦ + r H 3◦ .

(12)

r H 3◦

The value is the partial molar enthalpy of formation of HCl(sln) at the concentration given, and is calculated from the enthalpy of formation of the inﬁnitely dilute acid (Cox et al., 1989), the enthalpy of formation of the HCl solutions (Parker et al., 1976) and the densities of the HCl solution at 298.15 K (Söhnel and Novotný, 1985), neglecting the inﬂuence of the lanthanide ion. The second scheme involves the enthalpy of solution of the lanthanide sesquioxide and the lanthanide trihalide: Ln(cr) + 34 O2 (g) = 12 Ln2 O3 (cr) 1 3 2 Ln2 O3 (cr) + 3HCl(sln) = LnX 3 (sln) + 2 H2 O(sln) LnCl3 (cr) + (sln) = LnCl3 (sln) 3 3 2 H2 (g) + 2 Cl2 (g) = 3HCl(sln) 3 3 3 2 H2 (g) + 4 O2 (g) = 2 H2 O(sln) Ln(cr) + 32 Cl2 (g) = LnCl3 (cr)

r H 5◦ r H 6◦ r H 2◦ r H 3◦ r H 7◦ r H 4◦

174

R.J.M. KONINGS AND A. KOVÁCS

For this reaction sequence: f H ◦ (LnCl3 , cr, 298.15 K) = r H 5◦ + r H 6◦ + r H 3◦ − r H ◦7 − r H ◦2 , where r H ◦7 is the partial enthalpy of formation of H2 O(sln) in hydrochloric acid. Only in case the enthalpy of formation of the sesquioxide is based on the combustion of the lanthanide metal, the two schemes are really independent. For the calculation of the enthalpies of formation of the tribromides and triiodides, the same reaction cycles were used as for the trichlorides. However, as the halide ion in the compounds are different from those in the solution (e.g., LnI3 in HCl(aq)) the calculation of r H 3◦ becomes a bit more complex as we have to deal with the ternary system H2 O–HCl–HX. In that case, it is assumed that the apparent enthalpy of formation of HI and HBr in HCl solutions are the same as in HBr and HI solutions of the same molality. The results derived in this way by Cordfunke and Konings (2001b) are listed in tables B.1 to B.14 of Appendix B, the recommended values are given in table 12. For the trichlorides several studies have been reported for each compound, except, of course, PmCl3 . The results quite well agree after recalculation, often with more recent enthalpies of solution of the metals. This is especially true for the results derived from the early measurements by Bomer and Hohmann (1941a, 1941b) which generally deviate signiﬁcantly when the original value for the enthalpy of solution of the metal is used. This has been explained by the fact that the metals probably contained large fraction impurities, especially of potassium (Spedding and Miller, 1952). For the tribromides and triiodides the situation is less good. Often the number of studies is limited (e.g., for PrI3 and SmI3 only the measurements by Bommer and Hohmann (1941b)) or no measurements have been made (EuBr3 , EuI3, TmBr3 , YbI3 and LuBr3 , in addition to PmBr3 and PmI3 ). In general one can conclude that the enthalpies of solution of the metals form the major source of uncertainty. Cordfunke and Konings (2001b) tried to overcome this by combining results from different sources and by inter- or extrapolation values as a function of the molarity, which was possible in some cases because accurate determinations of the enthalpy of solution as a function of molarity were performed by Merli et al. (1998). But in some cases (e.g., the cerium trihalides) the analysis heavily relies almost completely on a single measurement. The variation of the enthalpies of formation of the trichlorides, tribromides and triiodides are shown in ﬁg. 24. The general patterns is the same as observed for the triﬂuorides. Also for the trichlorides, tribromides and triiodides the variation of the quantity {f H ◦ (LnX 3 , cr, 298.15 K) − f H ◦ (Ln3+ , aq, 298.15 K)} with the ionic radius has been examined, as shown in ﬁgs. 25 to 27. The results for the trichlorides clearly show a difference between the two crystallographic modiﬁcations, but for the tribromides and triiodides a difference is not very evident. The trends shown in ﬁgs. 25 to 27 have been used to estimate the enthalpies of formation of those compounds for which no or no reliable experimental data are available.

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

175

Fig. 24. The enthalpy of formation of the lanthanide trichlorides, tribromides and triiodides as a function of the atomic number. Estimated values are indicated by closed symbols.

Fig. 25. The quantity f H ◦ (LnCl3 , cr) − f H ◦ (Ln3+ , aq) as a function of the ionic radius (coordination number 6); , monoclinic and ◦ hexagonal structure.

6. Heat capacity of the liquid trihalides 6.1. LnF3 The essential thermodynamic quantity for the liquid trihalides is the heat capacity, which in combination with the data for the solid phase gives the enthalpy/entropy of fusion. With these two quantities the Gibbs energy of the liquid phase can be calculated and extrapolated to the super-cooled state, if needed. The enthalpy increment of the lanthanide triﬂuorides in the liquid phase has been measured for most compounds (see table 7). The heat capacity has been derived from these results by ﬁtting them to a 2-term equation {H ◦ (T ) − H ◦ (298.15 K)} = a(T /K) + b. In

176

R.J.M. KONINGS AND A. KOVÁCS

Fig. 26. The quantity f H ◦ (LnBr3 , cr) − f H ◦ (Ln3+ , aq) as a function of the ionic hexagonal, radius (coordination number 6); ⊕, orthorhombic and rhombohedral structure.

◦

Fig. 27. The quantity f H ◦ (LnI3 , cr) − f H ◦ (Ln3+ , aq) as a function of the ionic radius (coordination number 6); ⊕, orthorhombic and rhombohedral structure.

most cases a single set of data by Spedding and coworkers (Spedding and Henderson, 1971; Spedding et al., 1974) is available; only for CeF3 and HoF3 other measurements have been reported. For CeF3 the results of King and Christensen (1959) and Spedding et al. (1974) are in excellent agreement, for HoF3 the results of Spedding and Henderson (1971) and Lyapunov et al. (2000) disagree up to 6%. We have preferred the results of Spedding and Henderson (1971) for reasons given earlier.

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

177

Fig. 28. The heat capacity of the liquid lanthanide trihalides.

Figure 28 shows the trend in the heat capacity of the lanthanide triﬂuorides. The irregular pattern indicates a large excess term for the compounds with a partially ﬁlled lanthanide ion f -shell, suggesting that this is of an electronic nature, which is consistent with the strong ionic nature of these liquids. Not shown in ﬁg. 28 is the value for LaF3 derived from the experimental results. It is unrealistically high: 330.07 J·K−1 ·mol−1 . This is probably due to the fact that the experiments only cover a small temperature range (60 K) in which a post-melting effect cannot be excluded, especially in combination with the anomalous rapid increase already noted for the solid phase. Figure 28 shows that the trend in the lanthanide ﬂuorides (and other trihalides) suggests a value of about 135 J·K−1 ·mol−1 for LaF3 . The enthalpies of fusion that have been derived from the enthalpy increment equations for the solid and liquid phase are listed in table 13 and the derived entropies of fusion are plotted in ﬁg. 29. It can be seen that the enthalpies and entropies of fusion for ErF3 to LuF3 are signiﬁcantly lower than those of the other lanthanide triﬂuorides. Because these four compounds

178

R.J.M. KONINGS AND A. KOVÁCS Table 13 Enthalpy of fusion and heat capacity of the liquid phase for the lanthanide triﬂuorides

compound LaF3 CeF3 PrF3 NdF3 PmF3 SmF3 EuF3 GdF3 TbF3 DyF3 HoF3 ErF3 TmF3 YbF3 LuF3

Tfus /K 1766 1703 1670 1649 1605 1571 1549 1501 1446 1426 1416 1413 1431 1435 1455

fus H ◦ /kJ·mol−1 55.87 56.52 57.28 54.75 53.4 52.43 52.9 52.44 58.44 58.42 56.77 27.51 28.90 29.74 29.27

fus S ◦ /J·K−1 ·mol−1 31.51 33.19 34.30 33.20 33.3 33.37 34.2 34.94 40.41 40.97 40.09 19.47 20.20 20.73 20.12

V /Vcr a /% 29.14 32.92 29.13 30.78 25.58 25.81 25.35 26.57 28.37 29.99 31.95

Cp (liq) /J·K−1 ·mol−1 135b 130.61b,c 130.76b 172.82b 160 148.94d 130 115.20b 151.91d 156.92d 135.02b 146.83d 140.32d 121.70d 126.94b

a V = V − V where V is the volume of the liquid phase at the melting point and V the volume of the solid cr cr liq liq

phase at room temperature. Data are taken from Kishenbaum and Cahill (1960), Kishenbaum and Cahill (1962) and Khairulin et al. (2000). b Spedding et al. (1974). c King and Christensen (1959). d Spedding and Henderson (1971).

Fig. 29. The entropies of fusion (◦) and the sum of the transition and fusion entropies (•) of the LnF3 compounds.

undergo an orthorhombic to hexagonal transformation before melting, the sum of the transition and fusion entropies are plotted also. This quantity shows a steady but small increase along the lanthanide trihalide series, from which the enthalpies of fusion of PmF3 and EuF3 have been estimated. 6.2. LnCl3 For the liquid lanthanide trihalides data from enthalpy-increment measurements and heat capacity (DSC) measurements are available, as summarised in table C.1 of Appendix C, the recommended values are given in table 14. The majority of the results have been reported by two

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Table 14 Enthalpy of fusion and heat capacity of the liquid phase for the lanthanide trichlorides compound LaCl3 CeCl3 PrCl3 NdCl3 PmCl3 SmCl3 EuCl3 GdCl3 TbCl3 DyCl3 HoCl3 ErCl3 TmCl3 YbCl3 LuCl3

Tfus /K 1133 1090 1060 1032 994 950 894 875 855 924 993 1049 1095 1138 1198

fus H ◦ /kJ·mol−1 55.0b 53.6c 49.9b 49.2b 48.7 47.6 45.0 40.6b 19.5b 25.5b 32.6b 32.6d 35.6d 37.6 39.5

fus S ◦ /J·K−1 ·mol−1 48.54 49.17 47.12 47.67 49 50.1 50.3 46.40 22.80 27.75 32.83 31.08 32.51 33 33

V /Vcr a /% 19.1 18.0 21.0 21.8 24.5 26.4 21.0 0.3 1.3 4.9

Cp (liq) /J·K−1 ·mol−1 157.7b 161.05c 155.3b 149.5b 147 144.4d 142 139.7b 144.47b 144.77b 148.67b 141.00b 141 140 141

a Data taken from Iwadate et al. (1995) and Wasse and Salmon (1999b). b Dworkin and Bredig (1963a, 1963b, 1971). c Walden and Smith (1961). d Gaune-Escard et al. (1994, 1996).

different research groups: Dworkin and Bredig (1963a, 1963b, 1971) using drop calorimetry and Gaune-Escard et al. (Gaune-Escard et al., 1996; Rycerz and Gaune-Escard, 2002a, 2002b) using differential scanning calorimetry. The early results of Dworkin and Bredig (1963a, 1963b) were reported without details and could not be recalculated, in contrast to the later results. In general, the reliability of the results of both studies is limited since the measurements cover small temperature ranges. For NdCl3 and GdCl3 the studied temperature range is larger than 50 K, and the agreement is excellent; for PrCl3 and DyCl3 it is less than 25 K for the DSC measurement and the agreement is poor. The trend in the heat capacity of the lanthanide trichlorides is shown in ﬁg. 28. It is clear that the variation in the values is much less pronounced than in case of the triﬂuorides, the (apparent) electronic excess term being small. This suggests that the structure of the liquid trichlorides is different, i.e., less ionic. The structure of the liquid trichlorides has been studied extensively in recent years (Iwadate et al., 1995; Wasse and Salmon, 1999a, 1999b; Hutchinson et al., 1999; Wasse et al., 2000) by X-ray and neutron diffraction. The results of these studies indeed show that intermediate range order exists in the liquid trichlorides through the and eventually Ln2 Cl6−n formation of molecular species of the type LnCl3−n n n , yielding a loose ionic network. With decreasing cation size from La to Lu, the ionic character of the liquid reduces further, which is evidenced by the decrease of the electrical conductivity of the liquid trichlorides along the lanthanide series (Wasse and Salmon, 1999a). As is shown in ﬁg. 30 the variation in Cp (liq) of the hexagonal trichlorides can be correlated to the volume change between the solid (at room temperature) and the liquid: the heat

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Fig. 30. The heat capacity of liquid lanthanide trichlorides as a function of the volume change V /Vcr .

Fig. 31. The entropies of fusion of the LnCl3 compounds.

capacity is low when the volume change is large, indicating that part of the variation in Cp (liq) arises from variation in Clat . Thus the heat capacity of SmCl3 is estimated from the known V , that of PmCl3 and EuCl3 is interpolated. For the monoclinic trichlorides DyCl3 , HoCl3 and ErCl3 the volume change is quite small, which is due to the fact that these compounds undergo a solid-solid transformation before melting. The values for these compounds have been estimated from the trend suggested in ﬁg. 28. The entropies of fusion almost constant in the hexagonal LnCl3 series LaCl3 –GdCl3 , as shown in ﬁg. 31. From this trend we estimate fus S ◦ = 47 J·K−1 ·mol−1 for PmCl3 and SmCl3 . In the series TbCl3 to TmCl3 the entropy of fusion increases towards a constant value fus S ◦ = 33 J·K−1 ·mol−1 which we have taken for YbCl3 and LuCl3 . This observation is not in agreement with the experimental DTA data by Goryushkin et al. (1990) who observed a steady increase from TbCl3 to LuCl3 . We consider their data, however, not accurate enough. 6.3. LnBr3 and LnI3 There are only a few measurements of the heat capacity of the liquid tribromides and triiodides and most of them have been made by Dworkin and Bredig (1963a, 1963b, 1971) using drop calorimetry. Rycerz and Gaune-Escard (1999a) measured the heat capacity of LaBr3 (l)

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Table 15 Enthalpy of fusion and heat capacity of the liquid phase for the lanthanide tribromides and triiodides compound LaBr3 CeBr3 PrBr3 NdBr3 PmBr3 SmBr3 EuBr3 GdBr3 TbBr3 DyBr3 HoBr3 ErBr3 TmBr3 YbBr3 c LuBr3 LaI3 CeI3 PrI3 NdI3 PmI3 SmI3 EuI3 c GdI3 TbI3 DyI3 HoI3 ErI3 TmI3 YbI3 c LuI3

Tfus /K 1061 1005 965 955 930 913 978 1043 1102 1152 1192 1196 1228

fus H ◦ /kJ·mol−1 54.39a 51.88a 47.28a 45.61a 48.6 47.5 50.9 38.07 41.9 46.4b 50.21a 50.2 51.6

fus S ◦ /J·K−1 ·mol−1 51.26 51.62 48.94 47.76 52 52 52 35.98 38 40.31 41.98 42 42

V /Vcr a /%

Cp (liq) /J·K−1 ·mol−1 144.3a 149 154.8a 154.92a 155 149 144 139.46a 144 149 149 149 149

1298

51.8

42

144

1045 1033 1011 1059 1090 1123

55.45a 51.88a 53.14a 40.94a 43.6 47.2

53.26 50.22 52.56 38.66 40 42

151.77a 155 155 155.74a 155 155

1204 1229 1251 1267 1288 1294

53.97a 57.48a 56.5b 57.0 58.0 58.2

44.83 46.77 45.16 45 45 45

155.85a 157.50a 155 155 155 155

1323

59.5

45

155

a Dworkin and Bredig (1963b, 1971). b Cordfunke and Booij (1997). c Decomposes before melting.

in a very limited temperature range (1070–1090 K), obtaining a somewhat different value (151.12 J·K−1 ·mol−1 ). The results (ﬁg. 28) show that the variation in Cp (liq) along the lanthanide series becomes less prominent going from F to I, indicating that the character becomes increasingly less ionic and more molecular. The heat capacity of the liquid tribromides have therefore been assumed to show a slight trend, those of the triiodides to be approximately constant (table 15). The enthalpies of fusion of some hexagonal tribromides and orthorhombic triiodides have been measured by drop calorimetry (Dworkin and Bredig, 1963a, 1971). The en-

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tropies of fusion derived from these values is about 50 J·K−1 ·mol−1 for the ﬁrst group, and 52 J·K−1 ·mol−1 for the second, except for NdI3 . This compound, however, undergoes a solid state transition, as discussed before, and the sum of the entropies of transition and fusion is close (54 J·K−1 ·mol−1 ). For the orthorhombic tribromides no experimental data are available, and we have assumed the entropy of fusion to be close to that of the isostructural triiodides. The few data for the hexagonal/rhombohedral tribromides suggest an increase with increasing atomic number, whereas the few data for the hexagonal/rhombohedral triiodides suggest a constant value. This may be an indication that the high temperature phase behaviour for GdBr3 and TbBr3 is more complex. It should be noted that Goryushkin and coworkers (Goryushkin and Poshevneva, 1992, 1996; Goryushkin et al., 1999; Poshevneva et al., 2002) reported enthalpies and entropies of fusion of LuI3 , HoI3, ErI3, and SmI3 that are very different (fus S ◦ = 22.6 ± 3.0 J·K−1 ·mol−1 for SmI3 , 18 ± 4 J·K−1 ·mol−1 for HoI3 , 23 ± 2 J·K−1 ·mol−1 for ErI3 and 82 ± 20 J·K−1 ·mol−1 for LuI3 ). But since the results for the trichlorides by the same authors are in poor agreement with other experimental determinations, they have not been considered for the recommended values.

7. Heat capacity of the gaseous trihalides 7.1. LnX3 monomers The thermodynamic functions of the gaseous lanthanide trihalides have been calculated using standard statistical thermodynamic methods which relate the functions Cp , S, and H to the molecular partition function Q (Lewis et al., 1961): Q= (13) gi e−εi / kT , i

where εi is the energy of state i, which has a statistical weight (degeneracy) gi , k is the Boltzmann constant and T is the absolute temperature. Using the Bohr–Oppenheimer approximation, the energy can be described as the sum of the translational and the internal energies, the latter being the sum of the electronic, rotational and vibrational contributions. The total partition function thus becomes the product of the individual ones: Q = qtrs · qelec · qvib · qrot .

(14)

The calculation of thermodynamic functions thus requires accurate knowledge of the molecular geometry, the electronic and vibrational energy levels of the gaseous molecules. The electronic levels of the gaseous LnX 3 molecules have not been determined experimentally, but are estimated from those of the Ln3+ ions measured in the crystal phase (Myers and Graves, 1977a). For the molecular geometry and vibrational properties experimental data are available, though incomplete for the whole LnX 3 family. For that reason the experimental data were extended by empirical estimates (Myers and Graves, 1977a) or by results from quantum chemical computations (Joubert et al., 1998) in previous thermodynamic compilations. In this section we will discuss the structural and vibrational properties to derive a consistent set of

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183

Fig. 32. The bond length of the lanthanide trihalides; •, experimental values from ED (re ); ◦, experimental values from ED (rg ); , Adamo and Maldivi (1998) for the BP-DS/TZ, TZd level; ♦ Joubert et al. (1998) at the MP2/ECPD , VDZd level; Dolg et al. (1991) at the CISD + Q/ECPD f, ECPD d level; Adamo and Maldivi (1998) at the B3P/ECPS , ECPS d level. For details of the computations see original papers.

bond distances, bond angles and vibration frequencies for the thermodynamic calculations. For a more detailed analysis see the review by Kovács and Konings (2002). The structure and vibrational spectra of the lanthanide trihalides have been studied extensively in the past decade. Due to the recent developments in the experimental and theoretical

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Table 16 Ln–X equilibrium bond distances (pm)a Ln La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

LnF3 207.7 206.8 205.8 204.9 203.9 202.9 202.0 201.0 200.1 199.1 198.1 197.2 196.2 195.3 194.3

LnCl3 253.4 252.2 251.1 249.9 248.8 247.6 246.5 245.3 244.2 243.0 241.9 240.7 239.6 238.4 237.3

LnBr3 268.9 267.6 266.4 265.2 263.9 262.7 261.5 260.3 259.0 257.8 256.6 255.3 254.1 252.9 251.6

a Estimated uncertainty ±2 pm.

LnI3 286.7 285.7 284.8 283.8 282.9 281.9 280.9 280.0 279.0 278.1 277.1 276.1 275.2 274.2 273.3

Table 17 X–Ln–X equilibrium bond angles (in degrees)a Ln La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

LnF3 109.0 109.5 110.0 110.5 111.0 111.5 112.0 112.5 113.0 113.5 114.0 114.5 115.0 115.5 116.0

LnCl3 118.0 118.5 119.0 119.5 120.0 120.0 120.0 120.0 120.0 120.0 120.0 120.0 120.0 120.0 120.0

LnBr3 118.0 118.5 119.0 119.5 120.0 120.0 120.0 120.0 120.0 120.0 120.0 120.0 120.0 120.0 120.0

LnI3 118.5 119.0 119.5 120.0 120.0 120.0 120.0 120.0 120.0 120.0 120.0 120.0 120.0 120.0 120.0

a Estimated uncertainty: for LnF : ±4◦ ; for the 3 other halides: ±2◦ .

methods the accuracy of the data has been improved considerably. Many early experimental data have been reanalysed, and numerous computations have been performed on some “popular” LnX 3 species. The latest experimental and theoretical data, reviewed recently by the present authors (Kovács and Konings, 2002),1 conﬁrmed previously suggested trends (Myers and Graves, 1977a) and facilitated the estimation of the missing data of the non-investigated molecules or to correct non-reliable earlier ones. Based on the recent experimental and computed results we can make more accurate predictions than obtained previously (Myers and Graves, 1977a; Jia and Zhang, 1988). The available experimental data on the molecular geometries of the lanthanide trihalides are compiled in tables D.1 to D.4 of Appendix D. Equilibrium geometries (re , αe ) from electron diffraction (ED) experiments on 13 lanthanides trihalides have been reported by Zasorin (1988). More recent studies on lanthanide chlorides and bromides by Giricheva et al. (2000a, 2000b, 2000c, 2000d) and Zakharov et al. (2001) gave slightly shorter bond distances. The difference may arise from the neglect of the (small) dimer content of the vapour by Zasorin (Hargittai, 2000). However, the data from the two sources are close and agree within the given experimental errors. The experimental and selected computed r(Ln–X) bond lengths are presented in ﬁg. 32. The most important trend that is obvious from the ﬁgure is the gradual decrease of r(Ln–X) along the lanthanide row as a result of the well known “lanthanide contraction”. Although the computations indicate the same trend, they consistently overestimate the bond distances. The best probable values for the equilibrium geometrical parameters are given in tables 16 and 17. They take into account the opposite effects of dimer formation and the harmonic 1 For earlier reviews on the topic see those of Hargittai (2000) (molecular structure) and Boghosian and Papatheodorou (1996) (vibrational frequencies).

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185

Fig. 33. The computed potential energy curves for the LaX 3 molecules (Kovács and Konings, 1997a); β is the angle between the La–X bond and the symmetry axis; , LaCl3 ; ◦, LaBr3 ; , LaI3 .

approximation in the ED analysis, information on various trends, and the ﬂoppy nature of the LnX 3 molecules derived from quantum chemical computations. The latter property is the origin of the controversial results for the molecular symmetry of most LnX 3 species. Until recently (and apart from the early works) ED studies suggested a pyramidal C3v structure for all the lanthanide trihalides (see Zasorin (1988) and references therein). On the other hand, less sophisticated quantum chemical calculations (Cundari et al., 1995; Di Bella et al., 1993) suggested a planar D3h arrangement. The introduction of electron correlation and extended basis sets in the computations resulted generally (although not always) in a more pyramidal character of the LnX 3 species. An application of selectivity rules for the gas-phase IR spectra (Kovács and Konings, 1997a, 1997b) and the different symmetry number (3 for C3v and 6 for D3h ) in thermodynamic calculations were not conclusive either. Most of the recent experimental and computed results indicate a gradual increase of the X–Ln–X bond angle (towards the planar 120◦ ) from F to I and from La to Lu.2 This is in agreement with the decreasing polarizability of the ions along the lanthanide series and the weaker polarization abilities of the heavier halides. On the basis of the presently available results (Kovács and Konings, 2002) the LnF3 halides are most probably pyramidal (C3v ), as considerable pyramidal character was obtained by both experiment and computations, and the ν1 bands were found in the matrix-IR spectra. The absence of the ν1 bands in the IR spectra (Kovács and Konings, 1997a, 1997b), analysis of the shrinkage effect in CeI3 (Molnár et al., 1996) and the computed small inversion barriers for LaCl3 , LaBr3 and LaI3 (ﬁg. 33) imply a quasi-planar character for the trihalides of the light lanthanide elements. The most recent 2 For a comprehensive overview of the earlier results see the paper by Molnár and Hargittai (1995).

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experiments (Giricheva et al., 2000d, 2000c; Zakharov et al., 2001; Molnár et al., 1996) and sophisticated theoretical computations (Adamo and Maldivi, 1998; Adamo and Barone, 2000; Kovács, 2000; Solomonik and Marochko, 2000) indicate a D3h symmetry of the trichlorides, tribromides and triiodides of the heavier lanthanides. The exact border between pyramidal and planar structures cannot be determined presently. It would require highly sophisticated calculations with (nearly) complete electron correlation treatment and saturated basis set. The available experimental data on the molecular vibrations of lanthanide trihalides are compiled in tables D.1 to D.4 of Appendix D. Early gas-phase IR data on LaCl3 , PrCl3 , NdCl3 , and GdCl3 (Selivanov et al., 1973) have been extended recently by modern gas-phase Fourier-transform infrared measurements on several trichlorides and on the LaX3 and DyX3 (X = Cl, Br, I) series (Kovács and Konings, 1997a, 1997b; Groen, 2002), providing the ﬁrst experimental information on the symmetric bending ν2 frequencies of these compounds. They pointed out the error in interpretation of the early gas-phase IR spectra on NdX3 (X = Cl, Br, I) halides by Wells Jr. et al. (1977). In addition, numerous measurements have been performed on matrix-isolated LnX 3 species using infrared spectroscopy (Hauge et al., 1971; Hastie et al., 1975; Wesley and DeKock, 1971; Bencze et al., 1996; Feltrin and Cesaro, 1996; Perov et al., 1975; Loktyushina and Mal’tsev, 1984; Loktyushina et al., 1987) and in few cases Raman spectroscopy (Lesiecki et al., 1972; Groen, 2002). The data on DyX3 compounds (Groen, 2002) provided the ﬁrst experimental information on the symmetric stretching ν1 vibrations of the trichlorides, tribromides and triiodides. Note, that because of the high evaporation temperatures of LnF3 compounds only vibrational data of the matrix-isolated species could be obtained hitherto (Hauge et al., 1971; Hastie et al., 1975; Wesley and DeKock, 1971; Bencze et al., 1996). The experimental and selected computed vibrational frequencies of LnF3 and LnCl3 compounds are presented in ﬁgs. 34 and 35. The data show a gradually increase along the lanthanide row for all the four fundamentals. They conﬁrm also the earlier linear relationship suggested by Myers and Graves (1977a) for estimation of the frequencies. Our recommended values for the gas-phase vibrational frequencies are compiled in tables 18 to 21. Most of the estimated data have been derived from the available gas-phase and matrix-isolation vibrational spectra, the latter corrected for matrix-shifts. The LnF3 compounds deserve a special attention, because for these compounds no reference gas-phase vibrational spectra are available. Hastie et al. (1975) used the relationship νg = νNe + (0.8 ± 0.4)(νNe −νAr ) for the stretching frequencies suggested by Hastie et al. (1970), where νg is the gas-phase frequency. This formula is, however, not suited for general use as more recent experimental evidence indicates otherwise (see, e.g., the collected vibrational data by Hargittai (2000)). Furthermore, an excellent agreement is found between the gas-phase and Ar-matrix ν3 frequencies for the LnCl3 species, as shown in ﬁg. 35. In fact, the clue for the estimation of the gas-phase stretching frequencies of LnF3 compounds was provided by the computations. The overestimation of the Ln–F bond at the most reliable BP-DS/TZ,TZd level (Adamo and Maldivi, 1998) was found to be similar to that of the Ln–Cl bonds (cf. ﬁg. 32), thus a similar systematic error for the LnF3 and LnCl3 stretching frequencies can also be expected. For the LnF3 bending fundamentals ν4 and ν2 the mean of the Ne-matrix and Ar-matrix frequencies by Hastie et al. (1975) was accepted. Assumptions had to be made for the ν4

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187

Fig. 34. The vibrational frequencies of the lanthanide triﬂuorides; , recommended gas-phase frequencies; , experimental data for species isolated in neon matrix; , in argon matrix; , Adamo and Maldivi (1998) at the BP-DS/TZ, TZd level; ◦ Joubert et al. (1998) at the MP2/ECPD , VDZd level; Dolg et al. (1991) for the CISD + Q/ECPD f, ECPD d level; Adamo and Maldivi (1998) at the B3P/ECPS , ECPS d level.

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Fig. 35. The vibrational frequencies of the lanthanide trichlorides; •, experimental gas-phase values; , experimental data for species isolated in argon matrix; , in xenon matrix; , estimated gas-phase values; , Adamo and Maldivi (1998) at the BP-DS/TZ,TZd level; ◦ Joubert et al. (1998) at the MP2/ECP, VDZd level; Dolg et al. (1991) for the CISD + Q/ECPf, ECPd level; Adamo and Maldivi (1998) at the B3P/ECP, ECPd level.

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES Table 18 Vibrational frequencies (cm−1 ) for LnF3 moleculesa Ln La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

ν1 (A1 ) 532 536 540 544 548 552 556 560 564 568 572 576 580 584 588

ν2 (A1 ) 79 81 83 85 86 88 90 91 93 95 96 98 100 101 103

a Estimated uncertainty ±10 cm−1 .

ν3 (E) 501 506 511 516 521 526 531 536 541 546 551 556 561 566 572

ν4 (E) 123 125 127 128 130 132 133 135 137 138 140 142 143 145 147

189

Table 19 Vibrational frequencies (cm−1 ) for LnCl3 moleculesa Ln La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

ν1 (A1 ) 318 320 322 324 326 327 329 331 333 335 337 339 341 343 345

ν2 (A1 ) 59b 58c 60 60c 61 61c 63 64c 64 65c 66 66 67 68 69

ν3 (E) 317b 321c 320d 327c 328 331c 332 337c 337 340c 342 344 347 349 351

ν4 (E) 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98

a Estimated error for both the experimental and estimated data is ±10 cm−1 . b Measured by Kovács and Konings (1997a). c Measured by Kovács and Konings (1997b). d Measured by Selivanov et al. (1973).

frequencies of the bromides and iodides due to the lack of experimental data. Observations made for the LnF3 and LnCl3 series (the relative magnitude of the ν4 and ν2 frequencies, and the slightly larger slope for the trend in ν4 than that of ν2 ) have been extended to the LnBr3 and LnI3 molecules. This explains the larger uncertainty of the ν4 data for these molecules. The uncertainty of the ν2 values is due to the fact that the frequencies occur near the lower detection limit of most infrared spectrometers, thus excluding the observation of the complete band envelope in the spectra. On the basis of the systematic comparison of calculated and experimental results we conclude that present standard theoretical methods are not able to substitute gas-phase experiments on the geometrical and vibrational properties of the LnX 3 molecules. Systematic theoretical studies on the complete lanthanide series or on selected molecules (Cundari et al., 1995; Joubert et al., 1998; Dolg et al., 1991; Lanza and Fragalá, 1996; Adamo and Maldivi, 1997; Adamo and Maldivi, 1998; Adamo and Barone, 2000; Kovács, 2000) showed several deﬁciencies of the computational methods. These include the overestimation of the equilibrium Ln–X bond distance, uncertainty for the bond angles of planar/quasi-planar structures, a failure in predicting the values and trends of the ν2 mode. Moreover, the errors are not consistent for different halides, nor for the two (ν1 and ν3 ) stretching frequencies of an LnX 3 molecule. The less sophisticated character of the standard methods used at present shows that the computed results are quite sensitive to the theory and basis set chosen. On the other hand, the trends in the lanthanide row are predicted well by most advanced levels of theory. Furthermore, the error in the computed geometry and vibrational frequencies is strongly related.

190

R.J.M. KONINGS AND A. KOVÁCS Table 21 Vibrational frequencies (cm−1 ) of LnI3 moleculesa

Table 20 Vibrational frequencies (cm−1 ) of LnBr3 moleculesa Ln La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

ν1 (A1 ) 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221

ν2 (A1 ) 30b 36 36 37 37 37 38 38 39 44c 39 40 40 41 41

ν3 (E) 232b 233 234 236 237 238 239 241 242 243c 244 245 247 248 249

ν4 (E) 57 57 58 58 59 59 60 60 61 61 62 62 63 63 64

a Estimated error for the experimental ν values is 3 5 cm−1 , while for the experimental ν2 and estimated frequencies 10 cm−1 . b Measured by Kovács and Konings (1997a). c Measured by Groen (2002).

Ln La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

ν1 (A1 ) 162 163 163 164 164 165 165 166 166 167 167 168 168 168 169

ν2 (A1 ) 25b 27 28 28 28 28 28 29 29 32d 29 29 30 30 30

ν3 (E) 191b 191c 192 192 193 194 194 195 195 195d 196 197 198 198 199

ν4 (E) 40 41 41 41 42 42 42 42 43 43 43 44 44 44 45

a Estimated error for the experimental ν values is 3 5 cm−1 , while for the experimental ν2 and estimated frequencies 10 cm−1 . b Measured by Kovács and Konings (1997a). c Measured by Molnár et al. (1996). d Measured by Groen (2002).

Thus, computations can be used to extend partial experimental information. This was shown in joint experimental/computational studies using advanced theoretical methods (Kovács and Konings, 1997a, 1997b; Hargittai, 2000). 7.2. Ln2 X6 dimers The structure of the Ln2 X 6 dimers has been derived from electron diffraction (Molnár et al., 1996; Hargittai, 2000; Giricheva et al., 2000c, 2000b; Zakharov et al., 2001) and theoretical studies (Kovács, 1999, 2000, 2002) for a few species (table D.5). They indicated a bridged structure (D2h symmetry), as shown in ﬁg. 36. In most ED investigations a few geometrical

Fig. 36. The molecular geometry of the Ln2 X 6 dimer molecules.

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191

parameters were assumed to be identical to the monomers, the others were treated independently in the reﬁnements (Molnár et al., 1996; Giricheva et al., 2000c, 2000b; Zakharov et al., 2001). However, the small amount of dimeric molecules in the vapour makes such an analysis uncertain and quantum chemical calculations can therefore help to obtain more reliable data (Hargittai, 2000). High-level theoretical calculations indicate shorter terminal Ln–X bonds in the dimers (by ca. 1 pm) and longer ring Ln–X bonds (by ca. 20 pm) with respect to the bond in the monomers (Kovács, 2000). The recent results of Hargittai (2000) for Dy2 Cl6 and Dy2 Br6 are in very good agreement with the computations. Experimental information on the molecular vibrations of the dimers is restricted to a few, mostly, tentative assignments in matrix-IR spectra (Wesley and DeKock, 1971; Hastie et al., 1975; Feltrin and Cesaro, 1996). On the other hand, the complete vibrational spectrum has been computed for La2 X 6 , Dy2 X 6 , Ce2 Br6 and Ce2 I6 (Kovács, 1999, 2000; Kapala et al., 2002) and the data are summarised in table D.6. However, due to the failure of the computations to accurately predict the bending frequencies of the monomers at low wavenumbers, the reliability of these frequencies of the dimers may be limited also. Here we have used a rough approximation by calculating the thermodynamic functions of the Ln2 X 6 molecules from a single set of structural and molecular parameters for the ﬂuorides, chlorides, bromides and iodides each.

8. Enthalpy of formation of the gaseous trihalides 8.1. LnF3 The vapour pressures of all lanthanide triﬂuorides have been measured, including PmF3 . Various techniques have been used, which can be divided in indirect techniques (effusion and boiling point methods) which provide accurate data for the total vapour pressure, and direct mass spectrometric techniques, which are less precise, particularly in case of quadrupole mass spectrometry, but give information on the vapour composition and the presence of dimeric or polymeric molecules or dissociation products. The enthalpy of formation of the gaseous compounds can be derived from the vapour pressure studies using the thermal functions for the condensed and gaseous states derived in the previous sections. Third-law and second-law thermodynamic analyses of the equilibrium LnX 3 (cr, l) = LnX 3 (g)

(15)

have been applied, to derive the enthalpy of sublimation at 298.15 K, from which the enthalpy of formation of the gaseous compounds follows as: f H ◦ (LnX 3 , g) = subH ◦ + f H ◦ (LnX 3 , cr).

(16)

The third-law value for the enthalpy of sublimation is preferred in view of the accuracy of the thermal functions of the condensed and gaseous states presented in the previous sections, though it should be realised that all uncertainties/errors in the thermal functions (entropy, enthalpy) of solid as well as gaseous phase accumulate in this value. The results are presented in table E.1 of Appendix E.

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Fig. 37. The sublimation enthalpies at 298.15 K of the lanthanide triﬂuorides. Table 22 The selected enthalpies of formation of the kJ·mol−1 F Cl La −1254.7 ± 3.6 −734.1 ± 5.2 Ce −1262.4 ± 5.4 −729.3 ± 3.4 Pr −1253.6 ± 3.3 −729.3 ± 3.4 Nd −1246.2 ± 5.3 −716.4 ± 2.2 Pm −1245 ± 25 −710 ± 13 Sm −1240 ± 11 −710 ± 9 Eu −1175 ± 11 −625 ± 9 Gd −1245.4 ± 5.5 −712.2 ± 6.2 Tb −1245.1 ± 7.1 −712.9 ± 5.0 Dy −1243.5 ± 3.6 −708.9 ± 3.0 Ho −1246.3 ± 3.8 −712.9 ± 4.7 Er −1239.3 ± 2.8 −709.4 ± 8.2 Tm −1206.4 ± 5.8 −720.3 ± 6.5 Yb −1115.8 ± 5.4 −683 ± 9 Lu −1260.8 ± 5.4 −710.0 ± 2.5

gaseous lanthanide trihalides, in Br −596.5 ± 5.2 −584.5 ± 5.8 −587.5 ± 5.7 −562.3 ± 5.0 −560 ± 14 −562 ± 10 −477 ± 14 −563.5 ± 3.6 −570.9 ± 3.6 −561.3 ± 5.4 −562.1 ± 5.8 −566.0 ± 5.8 −560 ± 11 −522 ± 10 −547 ± 14

I −366.0 ± 8.2 −365.0 ± 5.2 −367.9 ± 5.8 −344.6 ± 5.0 −342 ± 14 −336 ± 11 −255 ± 14 −347.7 ± 8.5 −350.8 ± 6.5 −343.0 ± 5.0 −351.0 ± 6.7 −345.5 ± 6.7 −347.9 ± 6.9 −308 ± 10 −335 ± 10

Since most studies were made with indirect techniques assumptions had to be made on the fraction of dimeric molecules in the vapour. Mass spectrometric data are available only for La2 F6 and Ce2 F6 (Roberts and Searcy, 1972; Skinner and Searcy, 1971), and show a negligible fraction (10−4 ) of dimeric molecules in the vapour. On the basis of these observations we have derived the enthalpies of sublimation from the vapour pressure studies assuming only monomeric molecules to be present. The sublimation enthalpy of the triﬂuorides does not vary much in the lanthanide series (ﬁg. 37), but there is a small distinction between the start and the end of the LnF3 series. The values for LaF3 to NdF3 group around 440–430 kJ·mol−1 , the values for TbF3 to YbF3 around 450 kJ·mol−1 . These two groups correspond to the two different crystallographic modiﬁcations in the LnF3 series. The values of the compounds in between are less well deﬁned: for PmF3 to GdF3 only second-law values from mass spectrometric studies are available. These also group around 430 kJ·mol−1 except PmF3 which is somewhat higher, probably due to the uncertainties in the result for that compound, that was measured on a mixed (Pr1/3 Pm1/3 Sm1/3 )F3 sample (Gibson and Haire, 1989). Compared to the critical evaluation by Myers and Graves (1977b) the variation along the LnF3 series is much more smooth, which we feel is mainly due to the improved thermodynamic functions for the solid and gaseous phases derived in the present study.

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Fig. 38. The mean bond energy at 298.15 K of the lanthanide triﬂuorides.

The recommended enthalpies of formation of the gaseous triﬂuorides derived from these values are shown in table 22. From these values the mean bond energy can be derived as one third of the energy of the reaction: LnX 3 (g) = Ln(g) + 3X(g).

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Figure 38 shows the mean bond energy of gaseous triﬂuorides (for practical reasons expressed as the mean bond enthalpy at 298.15 K). It reveals a regular pattern: the bond energies of LaF3 , GdF3 and LuF3 (f0 , f7 and f14 conﬁgurations) are about equal, in between the bond energy systematically decreases reaching the lowest values at EuF3 and YbF3 , indicating that the bond energy becomes weaker with increasing number of electrons in the ﬁrst and second half of the f shell. This pattern (including the plateau for Dy–Ho–Er) is typical for many atomic properties of the lanthanide elements and ions (e.g., ionisation potential). 8.2. LnCl3 Also for the trichlorides a large number of vapour pressure studies have been made, and the results of the third-law analysis are shown in table E.2 of Appendix E. The formation of Ln2 Cl6 dimers in the vapours of LnCl3 (Ln = La, Eu, Lu) compounds has been demonstrated by Hastie et al. (1968) by mass spectrometry. They found that the dimer fraction, as derived from the ion-intensity data, is small for LaCl3 and EuCl3 (< 0.01), but indicate a dimer fraction of ∼ 0.02 in the vapour of LuCl3 . Kudin et al. (1997, 2000) studied the vapours of DyCl3 , TbCl3 , TmCl3 and YbCl3 by mass spectrometry. They concluded that for DyCl3 and TbCl3 the dimer fraction can be signiﬁcant (around 0.10 at 1600 K) whereas for TmCl3 and YbCl3 it is negligible. These authors also found evidence for the existence of higher polymers (trimers and tetramers) in vapour, but their contribution to the total vapour pressure is negligible. Giricheva et al. (2000c, 2000b) found that the dimer fraction is 0.03 for ErCl3 and 0.09 for LuCl3 by mass spectrometry. Kapala et al. (2002) studied the vapour phase of CeCl3 , PrCl3 , NdCl3 and DyCl3 by mass spectrometry and found dimer fractions smaller than 0.01 for the light lanthanide trichlorides, and ∼ 0.02 in the vapour of DyCl3 . The results of Pogrebnoi et al. (2001) for CeCl3 and SmCl3 conﬁrm this. In the ﬁrst approximation we have neglected the dimers in the vapour pressure analysis. On the basis of the mass spectrometric results this seems to be justiﬁed for the light lanthanide trichlorides, and good agreement is found for the enthalpies of sublimation derived from the

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various studies. For the heavy lanthanide trichlorides a comparison to the work of Kudin et al. can be made. The enthalpies of sublimation derived from their results are, however, very discordant. For DyCl3 and TmCl3 the difference in the enthalpies of sublimation is far beyond the possible effect of dimers. A sensitivity analysis shows that a correction of the monomer pressure of the effusion studies for a dimer fraction of 0.1 increases the enthalpy of sublimation by 2–3 kJ·mol−1 . But also for TbCl3 and YbCl3 , for which the dimer effect should be small on the basis of Kudin’s results, the agreement is poor. We therefore conclude that in these studies the conversion of ion intensity to pressure may not be correct for the heavy dimers. On the basis of these considerations and the absence of a reliable way to systematically quantify the dimer fraction, we have neglected the possible dimer contribution in the analysis, but have raised the uncertainty of the selected enthalpies of sublimation. Figure 39 shows the variation in the sublimation enthalpy of the trichlorides. On ﬁrst sight the values for the crystallographic modiﬁcations in the LnCl3 series seem to be different, like was the case for the triﬂuorides. The enthalpies of sublimation of the hexagonal trichlorides LaCl3 –NdCl3 are about 40 kJ·mol−1 higher than those of the monoclinic compounds. GdCl3 also has hexagonal crystal structure (ﬁg. 2), but its enthalpy of sublimation is close to that of the monoclinic forms. TbCl3 is orthorhombic, and its enthalpy of sublimation is also close to the monoclinic series though ﬁg. 11 suggest it is crystallographically more closely related to the hexagonal series. The enthalpy of sublimation of PmCl3 , SmCl3 and EuCl3 have been estimated from these data assuming that the enthalpy of sublimation gradually decreases from LaCl3 to GdCl3 . The approximate values for EuCl3 by Moriarity (1963), although probably subjected to decomposition, and for SmCl3 by Pogrebnoi et al. (2001) (the mass spectrometric measurements by the group of Kudin are generally discordant as can be seen for TbCl3 and DyCl3 in table E.2) might indicate that this leads to a small overestimation. Accurate measurements are needed to resolve this. A distinct difference can be noted when the variation in the enthalpy of sublimation along the LnCl3 series is compared to the results of the critical evaluation by Myers and Graves (1977b). The trend for the lanthanide trichlorides is almost linear in our analysis which is not the case in the analysis of Myers and Graves (1977b), who reported a pronounced difference in enthalpy at the mid of the series separating the hexagonal and the monoclinic lanthanide trichlorides. This observation can clearly be related to the distinct different entropies for the solid phase that were selected here, based on new experimental results. The recommended enthalpies of formation of the gaseous trichlorides derived from the selected enthalpies of sublimation are shown in table 22. The mean bond energies derived from these values is shown in ﬁg. 40, which reveals the same pattern as for the triﬂuorides, which should be explained by a f0 -f7 -f14 linear base variation and an excess contribution which is related to the changes in the electronic nature of the lanthanide(III) ions. 8.3. LnBr3 The number of vapour pressure studies of the tribromides is signiﬁcantly less. Gietmann et al. (1996) systematically measured the vaporization of the lanthanide bromides using mass spectrometry, showing the importance of the dimeric molecules in the vapour. For the light lanthanide tribromides (La, Ce, Nd) the fraction of dimers is around 0.01, but for TbBr3 it is 0.03,

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195

Fig. 39. The sublimation enthalpies at 298.15 K of the lanthanide trichlorides. ⊕ – experimental results for SmCl3 and EuCl3 that are not considered (see text).

Fig. 40. The mean bond energy at 298.15 K of the lanthanide trichlorides.

for HoBr3 it is 0.08, and for ErBr3 and TmBr3 it is 0.10. The results of Zakharov et al. (2003) for NdBr3 is in agreement with the above data (0.007) whereas Zakharov et al. (2001) found a lower fraction for ErBr3 (0.025). As mentioned in the section for the chlorides, such fractions would lead to an error of maximum 2–3 kJ·mol−1 in case the dimer contribution is neglected. The enthalpies of sublimation for the monomer derived from Gietmann’s results are generally in reasonable agreement with the values from the indirect measurements although they are almost systematically the lowest (contrary to what one expects), as shown in table E.3 of Appendix E. A comparison with the torsion effusion data of Piacente and coworkers (Brunetti et al., 1999, 2000; Villani et al., 2000a, 2000b; Piacente et al., 2002) for six lanthanide tribromides, shows a difference of 4–10 kJ·mol−1 , irrespectively of the dimer fraction. It is clear that the effect of the neglect of dimers in the third-law analysis is of the same order as or even smaller than the variation between the various authors, and this has been reﬂected in the uncertainty. The variation in ﬁg. 41 thus is partly due to systematic errors between the studies which are not eliminated due to the limited number of studies, which is especially true for the tribromides of Gd-Lu. Gietmann’s results indicate an almost constant value for this series, as do the results of Makhmadmurodov et al. (1975). The enthalpy of sublimation of PmBr3 , SmBr3 and EuBr3 has been estimated to decrease gradually from NdBr3 to GdBr3 . The recommended enthalpies of formation of the gaseous tribromides derived from the selected enthalpies of sublimation are shown in table 22. The mean bond energies derived from these values are shown in ﬁg. 42, which conﬁrms the general patterns found for the other trihalides.

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Fig. 41. The sublimation enthalpies at 298.15 K of the lanthanide tribromides.

Fig. 42. The mean bond energy at 298.15 K of the lanthanide tribromides.

8.4. LnI3 The early mass spectrometric studies for the lanthanide triiodides do not mention the dimer formation (Hirayama and Castle, 1973), but in later studies this effect was considered. Hirayama et al. (1976) found that the dimer fraction for LaI3 is negligible. Kaposi et al. (1983, 1986) found the dimer fraction to be 0.05 and 0.03 for DyI3 and HoI3 respectively, whereas Gietmann et al. (1996) found it to be 0.1 for HoI3 . Struck and Feuersanger (1991), Struck and Baglio (1992) reported mass spectra for CeI3 and TmI3 which demonstrate the presence of dimers, with ion-intensity ratios of < 0.01 and ∼ 0.03, respectively. The results for the last compound are in contrast to the large fraction of dimers reported by Dettingmeijer and Dielis (1988) for TmI3: 0.21 at 880 K to 0.43 at 1010 K. As discussed by Struck and Feuersanger (1991) quadrupole mass spectrometry, as used by Dettingmeijer and Dielis (1988), is suspect as the conversion from ion current to equilibrium partial pressure is difﬁcult. In absence of a good way to quantify the dimer fraction of the triiodides and the indication that it is probably below 0.1, the dimers have been neglected in the vapour pressure analysis (table E.4 of Appendix E), similar to the chlorides and bromides. The effect of such small fractions is within the variation between the results of these studies. The sublimation enthalpy of triiodides vary in a similar way as that of the tribromides (ﬁg. 43), showing the same pattern as the trichlorides and tribromides. The enthalpy of sublimation of PmI3 , SmI3 and EuI3 has been interpolated from the NdI3 –GdI3 data; that of YbI3 and LuI3 taken close to the values of the TbI3–TmI3 series. The recommended enthalpies of formation of the gaseous triiodides derived from these values are shown in table 22, the mean bond energies derived from these values in ﬁg. 44.

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197

Fig. 43. The sublimation enthalpies at 298.15 K of the lanthanide iodides.

Fig. 44. The mean bond energy at 298.15 K of the lanthanide triiodides.

8.5. Ln2 X6 dimers As was already discussed in the previous sections, dimeric molecules contribute signiﬁcantly (up to 10%) to the total vapour pressure of the lanthanide trihalides. However, experimental information is only available for a few systems, which is often highly uncertain. As a result it is difﬁcult to predict trends in the lanthanide series or estimate unknown values. The lanthanide tribromide series is an exception as Gietmann et al. (1996) made a systematic study by mass spectrometry. The enthalpies of dimerisation derived from this work are shown in ﬁg. 45. They are almost constant along the series, especially considering that the uncertainty (in the experimental data but also in the thermal functions of the gaseous dimers) is relatively large. Experimental data are also available for all the lanthanum trihalides (Roberts and Searcy, 1972; Hastie et al., 1968; Gietmann et al., 1996; Hirayama et al., 1976), which permits one to investigate the dimerisation enthalpies as a function of the halide atom. In ﬁg. 46 the enthalpies of dimerisation at 298.15 K derived from these studies are plotted as a function of the atomic weight of the halide ion. It can be seen

Fig. 45. The enthalpies of dimerisation at 298.15 K of the lanthanide tribromides as derived from the work of Gietmann et al. (1996).

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Fig. 46. The enthalpies of dimerisation at 298.15 K of the lanthanum trihalides.

that the dimerisation enthalpy increases linearly from F to I. These results are in excellent agreement with the dimerisation energies (0 K) for LaX3 and DyX3 molecules calculated by (Kovács, 2000). Although the dimerisation enthalpies seem to indicate the largest stability of the Ln2 F6 molecules among the Ln2 X 6 dimers, it should be realised, however, that the derived dimerisation enthalpies refer to 298.15 K and the computations refer to 0 K and thus do not include the entropy contribution that is important at the high temperatures of the experiments. In absence of more detailed information we suggest therefore that for practical reasons the enthalpies of dimerisation are treated constant in the different lanthanide halides series: −233 kJ·mol−1 for the triﬂuorides, −213 kJ·mol−1 for the trichlorides, −185 kJ·mol−1 for the tribromides, and −165 kJ·mol−1 for the triiodides. 9. Conclusions In the present chapter we have presented a careful evaluation of the thermodynamic and related properties of the lanthanide trihalides. It is shown that the properties of these compounds vary regularly within the four series (F to I) and in most cases clear trends are observed. The melting points in all four lanthanide trihalide series exhibit a minimum which shift from the heavy lanthanides to the light lanthanides as the atomic number of the halide increases. In the ﬂuoride series the minimum occurs at ErF3 , in the chloride series at TbCl3 , in the bromide series probably at SmBr3 , and in the iodide series at PrI3 . This minimum concurs with a change in the stable crystallographic structure, except for the bromide series in which the high temperature polymorphic behaviour is not known. The variation in the heat capacity and entropy of the solid lanthanide trihalides can be described by a lattice contribution that linearly varies with atomic number within each crystallographic class of compounds, and an excess contribution that depends on the electronic conﬁguration (crystal ﬁeld) of the lanthanide ions. A distinct difference is observed between

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199

the heat capacity and entropy of the hexagonal and monoclinic lanthanide trichlorides, which clearly correlates with a distinct difference in molar volume between the two modiﬁcations. Both effects are absent in the lanthanide triﬂuoride series. The enthalpies of formation of the solid lanthanide trihalides show a slight increase along the series, with anomalous values for the Eu and Yb compounds, which is due to the fact that Eu and Yb metals have divalent standard states and 88 and 46 kJ·mol−1 , respectively, is necessary to form the trivalent state (Gschneidner Jr., 1969; Johansson and Mårtensson, 1987). The properties of the liquid lanthanide trihalides depend strongly on the atomic number of the halide. The variation in the heat capacity of the lanthanide ﬂuorides indicates a strongly ionic behaviour of the melts with a concomittent irregular trend related to the electronic conﬁguration of the lanthanide ions. In the lanthanide chlorides, bromides and iodides the trend becomes systematically more constant, indicating an increasing molecular nature of the melts. The molecular parameters of the gaseous lanthanide trihalide molecules exhibit simple linear trends, with decreasing bond length and increasing vibrational frequencies as the atomic number of the lanthanide ion increases. This is in agreement with the well-known lanthanide contraction (Gschneidner Jr., 1989). The Ln–X bond energies of the lanthanide trihalide molecules are about equal for LaX 3, GdX 3 and LuX 3 (f0 , f7 and f14 conﬁgurations) within each halide series, but in between the bond energy systematically decreases reaching minimum values at EuX 3 and YbX 3. This indicates that the bond energy becomes weaker with increasing number of electrons in the ﬁrst and second half of the f shell. This pattern is typical for many atomic properties of the lanthanide elements and ions (e.g., ionisation potential). The enthalpies of dimerisation for the LnX 3 molecules are about constant within each halide series. Although the literature on the thermodynamic and related properties of the lanthanide trihalides on which our evaluation and conclusions are based is extensive, it is far from complete. As we have demonstrated in many instances the gaps in the experimental information can be ﬁlled with estimates (e.g., the standard entropies and the enthalpies of formation) based on the observed systematics. However, this is not always possible for the following reasons: – The polymorphism of the trichlorides, tribromides and triiodides is not sufﬁciently well known to make very reliable estimations and predictions at high temperatures. Further experiments to solve the polymorphism of the middle of the series are required. – The experimental basis for the recommended heat capacity of the tribromides and triiodides is marginal and more low- as well as high-temperature heat capacity measurements are required. – The lack of auxiliary data such as crystal ﬁeld energies for the tribromides and triiodides further limits the value of the semi-empirical approach used here to estimate high temperature heat capacities. – The experimental basis to derive the enthalpies of formation of the triﬂuorides is limited. The data selected here are based on the results of a single laboratory. Reliable experiments to verify the selected values and conﬁrm the suggested trend are needed. – The experimental data on the gaseous compounds are affected by the limited knowledge of the dimer fraction in the vapour. A systemic study is only available for the tribromides. In spite of these limits, the data presented here form a consistent and reliable basis for thermochemical analysis and modelling.

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The information presented in this chapter will be included in the material property database for f-elements and compounds (f -MPD) of the Institute of Transuranium Elements, which is accessible through internet.3 Complete thermodynamic tables can be retrieved at that site, which will be updated regularly with new information. Appendix A. The transition and melting points of the lanthanide trihalides Table A.1 Transition and melting temperatures for the lanthanide triﬂuorides authors LaF3 Spedding and Daane (1960) Porter and Brown (1962) Robinson and Cripe (1966) Jones and Shand (1968)a Spedding and Henderson (1971)b Dworkin and Bredig (1971) Nafziger et al. (1973) Sobolev et al. (1976a) Greis and Cader (1985) Stankus et al. (2000) selected value:

Ttrs /K

Tfus /K 1766 1763 1768 ± 10 1693 1766 ± 3 1768 ± 3 1760 ± 2 1773 1773 1766 1766 ± 3

CeF3 King and Christensen (1959) Spedding and Daane (1960) Porter and Brown (1962) Robinson and Cripe (1966) Jones and Shand (1968)a Spedding and Henderson (1971)b Sobolev et al. (1976a) Greis and Cader (1985) selected value:

1732 1703 1710 1698 ± 10 1670 1703 ± 3 1716 1709 1703 ± 3

PrF3 Spedding and Daane (1960) Robinson and Cripe (1966) Jones and Shand (1968)a Spedding and Henderson (1971)b Sobolev et al. (1976a) Greis and Cader (1985) selected value:

1668 1673 ± 10 1645 1672 ± 3 1677 1674 1670 ± 3

NdF3 Spedding and Daane (1960) Robinson and Cripe (1966) Jones and Shand (1968)a

3 http://www.f-elements.net

1647 1653 ± 10 1620 continued on next page

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Table A.1, continued from previous page authors Spedding and Henderson (1971)b Sobolev et al. (1976a) Greis and Cader (1985) Stankus et al. (2000) selected value: SmF3 Spedding and Daane (1960) Thoma and Burton (1966) Jones and Shand (1968)a Spedding and Henderson (1971)b Gogadze et al. (1972a) Sobolev et al. (1976a) Greis and Cader (1985) Stankus et al. (2000) selected value: EuF3 Spedding and Daane (1960) Thoma and Burton (1966) Jones and Shand (1968)a Spedding and Henderson (1971)b Greis and Cader (1985) selected value: GdF3 Spedding and Daane (1960) Porter and Brown (1962) Thoma and Burton (1966) Jones and Shand (1968)a Spedding and Henderson (1971)b Zhigarnovskii and Ippolitov (1970a) Gogadze et al. (1972b) De Kozak et al. (1973) Pastor and Robinson (1974) Sobolev et al. (1976a) Greis and Cader (1985) Stankus et al. (1999) selected value: TbF3 Spedding and Daane (1960) Thoma and Burton (1966) Jones and Shand (1968)a Spedding and Henderson (1971)b Sobolev et al. (1976a) Greis and Cader (1985) selected value:

Ttrs /K

Tfus /K 1650 ± 3 1645 1651 1649 1649 ± 3 1579

828 852 762 ± 3 743 753 ∼760 743 ± 3

1568 1571 ± 3 1583 ± 5 1577 1582 1572 1571 ± 3 1549

973 954 1125 973 ± 3

1536 1549 ± 3 1531 1549 ± 3 1504 1501

1173 1074 1347 ± 3 1338 ± 5 1293 ± 5 1348 ± 5 1343 1338 1310 1347 ± 3

1516 1503 ± 3 1478 ± 5 1523 ± 5 1503 1501 1508 1509 ± 3 1501 ± 3 1445

1223 ± 6 1235

1477 1446 ± 3 1439 1455 1446 ± 3 continued on next page

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Table A.1, continued from previous page authors DyF3 Spedding and Daane (1960) Thoma and Burton (1966) Jones and Shand (1968)a Spedding and Henderson (1971)b Gogadze et al. (1972a) Pastor and Robinson (1974) Sobolev et al. (1976a) De Kozak and Almai (1978) Greis and Cader (1985) Khairulin et al. (1998) selected value: HoF3 Spedding and Daane (1960) Thoma and Burton (1966) Jones and Shand (1968)a Spedding and Henderson (1971)b Shaimuradov et al. (1974) Pastor and Robinson (1974) Sobolev et al. (1976a) Sobolev et al. (1976c) Greis and Cader (1985) Stankus et al. (2000) selected value:

Ttrs /K

Tfus /K 1427

1303 ± 6 1418

1432 1428 ± 3 1381 ± 5 1433 1420 1438 1433 1427 ± 5 1426 ± 3 1416

1343 ± 6

1343

ErF3 Spedding and Daane (1960) Thoma and Burton (1966) Jones and Shand (1968)a Spedding and Henderson (1971)b Gogadze et al. (1972c) Sobolev et al. (1976a) Sobolev et al. (1976c) Greis and Cader (1985) Stankus et al. (2000) selected value:

1348 1372 1388 ± 3 1369 ± 5 1377 1390 1392 1372 1388 ± 3

TmF3 Spedding and Daane (1960) Thoma and Burton (1966) Jones and Shand (1968)a Spedding and Henderson (1971)b Sobolev et al. (1976a) Greis and Cader (1985) selected value:

1303 1298 1325 ± 3 1320 1322 1325 ± 3

1407 1416 ± 3 1418 1423 1413 1413 ± 5 1420 1416 1416 ± 3 1413 1404 1416 ± 3 1418 ± 5 1407 1413 1420 1414 1413 ± 3 1431 1415 1416 ± 3 1432 1431 1431 ± 3 continued on next page

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Table A.1, continued from previous page authors YbF3 Spedding and Daane (1960) Thoma and Burton (1966) Jones and Shand (1968)a Zhigarnovskii and Ippolitov (1970b) Spedding and Henderson (1971)b Gogadze et al. (1972c) Labeau et al. (1974) Sobolev et al. (1976a) Greis and Cader (1985) Stankus et al. (1999) selected value:

Ttrs /K

1258 1245 1273 ± 7 1267 ± 3 1273 ± 5 1251 1251 1259 1256 1267 ± 3

LuF3 Spedding and Daane (1960) Thoma and Burton (1966) Jones and Shand (1968)a Spedding and Henderson (1971)b Sobolev et al. (1976a) Greis and Cader (1985) Stankus et al. (2000) selected value:

1218 1152 1230 ± 3 1226 1216 1220 1230 ± 3

Tfus /K 1430 1445 1416 ± 3 1418 ± 5 1438 1428 1445 1440 ± 5 1435 ± 5 1455 1456 1457 ± 3 1455 1453 1461 1455 ± 3

a Results published in graphical form only. b Also reported by Henderson (1970).

Table A.2 Transition and melting temperatures for the lanthanide trichlorides authors LaCl3 Spedding and Daane (1960) Dworkin and Bredig (1963a) Vogel and Schneider (1972) Nisel’son and Lyzlov (1976) Lyzlov and Nisel’son (1978) Seifert et al. (1985) Laptev et al. (1986) Igarashi and Mochinaga (1987) Gaune-Escard et al. (1994) selected value: CeCl3 Spedding and Daane (1960) Dworkin and Bredig (1971) Nisel’son and Lyzlov (1976) Laptev et al. (1986) Seifert et al. (1988a) Gaune-Escard et al. (1994) selected value:

Ttrs /K

Tfus /K 1135 1131 1123 1125 1125 1117 1118 1150 1127 1133 ± 5 1090 1090 1104 1092 1104 1086 1090 ± 2 continued on next page

204

R.J.M. KONINGS AND A. KOVÁCS

Table A.2, continued from previous page authors PrCl3 Spedding and Daane (1960) Dworkin and Bredig (1963a) Nisel’son and Lyzlov (1976) Laptev et al. (1986) Igarashi and Mochinaga (1987) Seifert et al. (1987) Gaune-Escard et al. (1994) selected value:

Ttrs /K

Tfus /K 1059 1059 1051 1051 1059 1062 1061 1060 ± 2

NdCl3 Spedding and Daane (1960) Druding and Corbett (1961) Dworkin and Bredig (1963a) Vogel and Schneider (1972) Nisel’son and Lyzlov (1976) Lyzlov and Nisel’son (1978) Laptev et al. (1986) Igarashi and Mochinaga (1987) Seifert et al. (1988b) Gaune-Escard et al. (1994) selected value:

1031 1031 1032 1032 1027 1027 1043 1029 1037a 1032 1032 ± 2

SmCl3 Spedding and Daane (1960) Korshunov et al. (1964) Vogel and Schneider (1972) Nisel’son and Lyzlov (1976) Laptev et al. (1986) Thiel and Seifert (1988) Rycerz and Gaune-Escard (2002a) selected value:

955 938 941 941 948 941 950 950 ± 5

EuCl3 Spedding and Daane (1960) Korshunov et al. (1966a) Laptev et al. (1986) Kiseleva et al. (1990) Seifert and Sandrok (1991) Rycerz and Gaune-Escard (2002b) selected value:

decomposes 896 893 905 ± 7 893 894 894 ± 3

GdCl3 Spedding and Daane (1960) Harris and Veale (1965) Korshunov and Drobot (1965) Dworkin and Bredig (1971) Vogel and Schneider (1972)

373 ± 10

875 873 ± 10 882 875 873 continued on next page

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

205

Table A.2, continued from previous page authors Nisel’son and Lyzlov (1976) Lyzlov and Nisel’son (1978) Garton and Walker (1982) Igarashi and Mochinaga (1987) Daniel et al. (1989) Goryushkin et al. (1990) Seifert et al. (1991) Gaune-Escard et al. (1994) selected value: TbCl3 Spedding and Daane (1960) Korshunov et al. (1966a) Dworkin and Bredig (1971) Lyzlov and Nisel’son (1978) Garton and Walker (1982) Goryushkin et al. (1990) Rycerz and Gaune-Escard (1999b) Morrison et al. (2000) selected value: DyCl3 Spedding and Daane (1960) Korshunov and Drobot (1965) Dworkin and Bredig (1971) Lyzlov and Nisel’son (1978) Garton and Walker (1982) Igarashi and Mochinaga (1987) Goryushkin et al. (1990) Gaune-Escard et al. (1996) Reuter and Seifert (1994) selected value: HoCl3 Spedding and Daane (1960) Korshunov et al. (1966b) Dworkin and Bredig (1971) Garton and Walker (1982) Goryushkin et al. (1990) Roffe and Seifert (1997) selected value: ErCl3 Spedding and Daane (1960) Korshunov et al. (1966b) Dworkin and Bredig (1971) Vogel and Schneider (1972) Lyzlov and Nisel’son (1978) Goryushkin et al. (1990)

Ttrs /K

Tfus /K 901 901 882 875

870–875

872 ± 10 770 783 ± 2 801 793.1 ± 4.7 790 ∼ 783 783 ± 5

611 611 ± 5

886.1 ± 3.3 878 873 875 ± 2 855 851 855 ± 2 868 860 856.9 ± 4.7 854 855 ± 3 920 927 924 ± 2 921 920 928 929.4 ± 6.8 909 919 924 ± 3 993 991 993 ± 2 977 1014.3 ± 3.4 973 993 ± 3 1049 1037 1049 ± 2 1035 1054 1064.0 ± 3.0 continued on next page

206

R.J.M. KONINGS AND A. KOVÁCS Table A.2, continued from previous page

authors Büchel et al. (1995) Gaune-Escard et al. (1996) Dudek and Seifert (2001) selected value:

Ttrs /K 1025

Tfus /K 1024 1046 1024 1049 ± 5

TmCl3 Spedding and Daane (1960) Goryushkin et al. (1990) Gaune-Escard et al. (1996) selected value:

1097 1110.2 ± 3.5 1092 1095 ± 3

YbCl3 Spedding and Daane (1960) Goryushkin et al. (1990) selected value:

1138 1155.5 ± 1.6 1138 ± 5

LuCl3 Spedding and Daane (1960) Lyzlov and Nisel’son (1978) Goryushkin et al. (1990) selected value:

1198 1177 1179.4 ± 2.4 1198 ± 5

a Value taken from the graphs, in the text 1104 K is given.

Table A.3 Transition and melting temperatures for the lanthanide tribromides authors LaBr3 Spedding and Daane (1960) Shimazaki and Niwa (1962) Dworkin and Bredig (1971) Rycerz and Gaune-Escard (1999a) selected value: CeBr3 Spedding and Daane (1960) Shimazaki and Niwa (1962) Thoma and Burton (1966) Dworkin and Bredig (1971) selected value: PrBr3 Spedding and Daane (1960) Dworkin and Bredig (1971) selected value:

Ttrs /K

Tfus /K 1062 1056 1061 ± 2 1058 1060 ± 3 1005 1005 995 1005 ± 2 1005 ± 2 964 966 ± 2 965 ± 3 continued on next page

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

207

Table A.3, continued from previous page authors NdBr3 Spedding and Daane (1960) Shimazaki and Niwa (1962) Dworkin and Bredig (1971) Cordfunke et al. (1999) selected value:

Ttrs /K

Tfus /K 955 957 955 ± 2 953.2 ± 0.3 955 ± 2

SmBr3 Spedding and Daane (1960) selected value:

913 913 ± 5

EuBr3 Spedding and Daane (1960) Thoma and Burton (1966) selected value:

decomposes 978 978 ± 10

GdBr3 Spedding and Daane (1960) Thoma and Burton (1966) selected value:

1043 1058 ± 2 1043 ± 5

TbBr3 Spedding and Daane (1960) Thoma and Burton (1966) selected value:

1101 1103 ± 2 1102 ± 3

DyBr3 Spedding and Daane (1960) Cordfunke and Blacquère (1997) selected value:

1152 1151.0 ± 1.5 1152 ± 3

HoBr3 Spedding and Daane (1960) Dworkin and Bredig (1971) Gietmann et al. (1996) selected value:

1192 1192 ± 2 1202 1192 ± 3

ErBr3 Spedding and Daane (1960) selected value:

1196 1196 ± 5

TmBr3 Spedding and Daane (1960) Thoma and Burton (1966) selected value:

1227 1228 ± 2 1228 ± 3

LuBr3 Spedding and Daane (1960) Thoma and Burton (1966) selected value:

1298 1233 ± 2 1298 ± 5

208

R.J.M. KONINGS AND A. KOVÁCS

Table A.4 Transition and melting temperatures for the lanthanide triiodides authors LaI3 Spedding and Daane (1960) Corbett et al. (1962) Shimazaki and Niwa (1962) Dworkin and Bredig (1971) Kutscher and Schneider (1971) selected value:

Ttrs /K

1045 1051.5 1034 1051 ± 2 1041 1045 ± 3

CeI3 Spedding and Daane (1960) Corbett et al. (1962) Dworkin and Bredig (1963a) Konings and Kok-Scheele (1999) selected value:

1039 1033–1034 1033 ± 2 1027 ± 1 1033 ± 2

PrI3 Spedding and Daane (1960) Shimazaki and Niwa (1962) Dworkin and Bredig (1963a) Kutscher and Schneider (1971) Corbett (1972) selected value: NdI3 Spedding and Daane (1960) Druding and Corbett (1961) Shimazaki and Niwa (1962) Dworkin and Bredig (1963a) Kutscher and Schneider (1971) Corbett (1972) Cordfunke et al. (1999) selected value: SmI3 Spedding and Daane (1960) Kutscher and Schneider (1971) Molodkin et al. (1984) Poshevneva et al. (2002) selected value: GdI3 Spedding and Daane (1960) Mee and Corbett (1965) Kutscher and Schneider (1971) Dworkin and Bredig (1971) Corbett (1972) selected value:

Tfus /K

1010 1006 1011 ± 2 1003 1011 1011 ± 2

847 847 ± 2 836 859.3 ± 0.6 859 ± 3

943

943 ± 10

1021 1013 ± 2 1013 ± 5

1057 1060 1048 1060 ± 2 1053 1060 1058.7 ± 0.6 1059 ± 2 1123 1089–1097a 1144–1155 1145 ± 9 1123 ± 5 1198 1204 1213 1204 ± 2 1204 1204 ± 3 continued on next page

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

209

Table A.4, continued from previous page authors TbI3 Spedding and Daane (1960) Dworkin and Bredig (1971) selected value: DyI3 Spedding and Daane (1960) Kutscher and Schneider (1971) Corbett (1972) Cordfunke and Blacquère (1997) selected value:

Ttrs /K

Tfus /K

1080 ± 2 1080 ± 5

1230 1228 ± 2 1229 ± 3 1251 1250 1256 1251.5 ± 1.5 1251 ± 3

1246 1101 1101 ± 5

HoI3 Spedding and Daane (1960) Gietmann et al. (1996) Goryushkin and Poshevneva (1996) selected value:

1267 1283 1266 ± 2 1267 ± 5

ErI3 Spedding and Daane (1960) Corbett (1972) Goryushkin et al. (1999) selected value:

1288 1287 1282 ± 10 1288 ± 3

TmI3 Spedding and Daane (1960) selected value:

1294 1294 ± 5

LuI3 Spedding and Daane (1960) Goryushkin and Poshevneva (1992) selected value:

1323 1313 ± 15 1323 ± 5

a Under decomposition.

Appendix B. The enthalpies of formation of the solid lanthanide trihalides Table B.1 The enthalpy of formation of LaX 3 (cr) at 298.15 K; H ◦1 and H ◦2 are the enthalpies of solution of La(cr) and LaX 3 (cr) in HCl(aq), respectively authors LaF3 Polyachenok (1967) Kondrat’evb Khanaev et al. (1977) Rezukhina et al. (1974) Johnson et al. (1980) selected value:

methoda H S S E C

H ◦1 /kJ·mol−1

H ◦2 /kJ·mol−1

f H ◦ /kJ·mol−1 −1695 −1698.2 ± 6.3 −1630.1 ± 5.0 −1731.8 ± 5.0 −1699.5 ± 2.0 −1699.5 ± 2.0 continued on next page

210

R.J.M. KONINGS AND A. KOVÁCS

Table B.1, continued from previous page H ◦1 /kJ·mol−1

H ◦2 /kJ·mol−1

f H ◦ /kJ·mol−1

S (0.1)

−738.5 ± 2.6

−132.2 ± 0.1

Lohr and Cunningham (1951) Spedding and Flynn (1954) Montgomery (1959)

S (1.5) S (0.27) S (0.51)

−695.0 ± 5.9 −705.7 ± 0.2

−1105.1 ± 2.6 −1072.2 ± 2.7c

−130.3 ± 0.7 −129.7 ± 0.4

Fitzgibbon et al. (1965) Gvelesiani and Yashvili (1967) Morss (1969) Laptev et al. (1990) Cordfunke and Booij (1995)

S (1.0) S (1.0) S (1.5) S (1.0) E S (1.0)

−705.5 ± 1.3 −708.0 ± 2.0 −708.8 ± 1.4 −703.3 ± 3.8

−1073.0 ± 0.9 −1070.2 ± 0.7d −1070.3 ± 1.6g

Oppermann et al. (1997)

S (4.0)

Merli et al. (1998)

S (1.0) S (6.0)

authors LaCl3 Bommer and Hohmann (1941a, 1941b)

methoda

−126.4 ± 0.5 −111.8 ± 0.4 −704.4 ± 1.2 −707.8 ± 1.2

−1071.6 ± 1.5

selected value: LaBr3 Hurtgen et al. (1980)

Oppermann et al. (1997) selected value:

S (1.0)

−158.5 ± 0.2

S (0.1) S (4.0)

−163.7 ± 0.4 −146.1 ± 0.4i

LaI3 Hohmann and Bommer (1941)

S (0.1)

Furkaliouk et al. (1995)

S (1.0)

Oppermann et al. (1997) selected value:

S (4.0)

−738.5 ± 2.6

−1066.9 ± 1.1 −1072.3 ± 1.5e −1071.1 ± 1.4f −1065.9 ± 0.6d −1069.4 ± 1.3g

−200.6 ± 0.7

[−196.6 ± 1.1]h −167.5 ± 0.4j

−905.1 ± 1.4e −904.0 ± 1.2f −902.3 ± 0.7c −902.8 ± 1.2d −904.4 ± 1.5 −706.5 ± 2.7 −671.9 ± 1.7c −667.9 ± 1.6 −673.9 ± 1.6e −689.4 ± 1.1d −673.9 ± 2.0

a E: e.m.f. measurements, S: solution calorimetry; values in parentheses give the concentration of the solvent in mol·dm−3 ; H: high temperature equilibria. b Kondrat’ev Y.V., Thesis, University of Leningrad. Cited and recalculated by Johnson et al. (1980). c Using H ◦ from Spedding and Flynn (1954). 1 d Cycle based on H ◦ (La O (cr)). f 2 3 e Using H ◦ from Merli et al. (1998). 1 f Using H ◦ from Fitzgibbon et al. (1965). 1 g Using H ◦ extra- or interpolated from the results of Merli et al. (1998). 1 h Derived from Furkaliouk et al. (1995). i In HBr(aq). j In HI(aq).

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

211

Table B.2 The enthalpy of formation of CeX 3 (cr) at 298.15 K; H ◦1 and H ◦2 are the enthalpies of solution of Ce(cr) and CeX 3 (cr) in HCl(aq), respectively authors CeF3 Kholokhova and Rezukhina (1976) selected value: CeCl3 Bommer and Hohmann (1941a, 1941b) Spedding and Miller (1952) Montgomery (1962) Laptev et al. (1990) Cordfunke and Booij (1995) selected value: CeBr3 Furkaliouk and Cordfunke (1996)

methoda

H ◦1 /kJ·mol−1

H ◦2 /kJ·mol−1

−1732.6 ± 4.2 −1689.2 ± 5.0b

E

S (0.1)

−726.8 ± 2.9

−136.8 ± 0.7

S (0.24) S (0.37) S (1.5) E S (0.24)

−699.2 ± 0.2

−137.1 ± 0.4 −134.2 ± 0.9 −129.4 ± 0.3

−690.9 ± 0.6

−136.24 ± 0.48

−168.87 ± 0.38

S (0.25)

selected value: CeI3 Hohmann and Bommer (1941)

S (0.1)

Furkaliouk and Cordfunke (1996)

S (1.0)

−726.8

−690.4 ± 2.9 −206.8 [−200.0 ± 0.9]f

selected value:

f H ◦ /kJ·mol−1

−1088.8 ± 3.0 −1061.1 ± 0.8c −1059.6 ± 0.5 −1058.9 ± 0.7 −1029.2 ± 0.7 −1060.5 ± 0.6c −1059.7 ± 1.5 −891.5 ± 0.8c −891.4 ± 1.0d −890.7 ± 1.7e −891.2 ± 1.5

−662.8 −669.4 ± 0.9 −667.3 ± 1.0c −666.4 ± 1.9e −666.8 ± 3.0

a E: e.m.f. measurements, S: solution calorimetry; values in parentheses give the concentration of the solvent in mol·dm−3 . b See main text for explanation of selected value. c Using H ◦ from Spedding and Flynn (1954). 1 d Recalculation of the reaction cycle in Cordfunke and Booij (1995) based on KCl/KBr. e Chloride cycle using H ◦ (CeCl ) from Cordfunke and Booij (1995). 3 1 f Derived from the enthalpy of solution of a CeI /KCl mixture. 3

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R.J.M. KONINGS AND A. KOVÁCS

Table B.3 The enthalpy of formation of PrX 3 (cr) at 298.15 K; H ◦1 and H ◦2 are the enthalpies of solution of Pr(cr) and PrX 3 (cr) in HCl(aq), respectively authors PrF3 Polyachenok (1967) Kondrat’evb Rezukhina et al. (1974) Johnson et al. (1980) selected value: PrCl3 Bommer and Hohmann (1941a, 1941b)

methoda

H ◦1 /kJ·mol−1

H ◦2 /kJ·mol−1

f H ◦ /kJ·mol−1 −1678 −1689.0 ± 6.3 −1712.0 ± 5.0 −1689.1 ± 2.6 −1689.1 ± 2.6

H S E C

S (0.1)

−723.4 ± 1.1

−141.8 ± 2.2

Lohr and Cunningham (1951) Spedding and Flynn (1954)

S (1.5) S (0.25) S (1.47)

−687.9 ± 9.6 −704.1 −692.8

−1081.1 ± 2.5 −1061.8c

−142.2 ± 0.6 −125.6 ± 0.9

Stubbleﬁeld (1969) Fitzgibbon et al. (1973) Laptev et al. (1990) selected value:

S (1.0) S (2.0) E

−687.9 ± 3.4 −692.2 ± 1.3

−1059.4 −1057.7 −1052.6 ± 9.6d

PrBr3 Hurtgen et al. (1980)

S (1.0) S (0.25) S (0.1)

−1035.9 ± 1.1 −1058.6 ± 1.5 −171.7 ± 0.7 [−174.8 ± 0.6]f −176.3 ± 0.4

−874.3 ± 3.4e −890.5 ± 4.0c −889.9g −890.5 ± 4.0

−208.9 ± 0.1

−683.1 ± 1.1 −664.7 ± 2.0c −664.7 ± 5.0

selected value: PrI3 Hohmann and Bommer (1941) selected value:

S (0.1)

−723.4 ± 1.1

a E: e.m.f. measurements, S: solution calorimetry; values in parentheses give the concentration of the solvent in mol·dm−3 ; H: high temperature equilibria. b Kondrat’ev Y.V., Thesis, University of Leningrad. Cited and recalculated by Johnson et al. (1980). c Using H ◦ from Spedding and Flynn (1954). 1 d Using H ◦ from Lohr and Cunningham (1951). 1 e Using H ◦ from Stubbleﬁeld (1969). 1 f Estimated by interpolation. g Using H ◦ from Bommer and Hohmann (1941a). 1

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

213

Table B.4 The enthalpy of formation of NdX 3 (cr) at 298.15 K; H ◦1 and H ◦2 are the enthalpies of solution of Nd(cr) and NdX 3 (cr) in HCl(aq), respectively authors NdF3 Polyachenok (1967) Kondrat’evb Kholokhova and Rezukhina (1976) Khanaev et al. (1977) Johnson et al. (1980) Kim and Oishi (1980) selected value:

methoda

H ◦1 /kJ·mol−1

H ◦2 /kJ·mol−1

−1653 −1678.1 ± 2.1 −1712.9 ± 4.2 −1650.6 ± 4.6 −1679.4 ± 1.9 −1660.6 ± 4.9 −1679.4 ± 1.9

H S E S C C

NdCl3 Bommer and Hohmann (1941a, 1941b)

S (0.1)

Spedding and Miller (1952) Polyachenok and Novikov (1963a) Stuve (1965a) Popova and Monaenkova (1989) Tiﬂova (1990) Cordfunke et al. (1996)

S (0.25) S (0.2) S (4.0) S (2.19) S (2.3) S (2.3)

−717.1 ± 4.3 [−688.0 ± 2.5]g −680.3 ± 0.8 −685.8 ± 5.4 −693.6 ± 0.9 −686.8 ± 1.0 −690.8 ± 1.6

−150.2 ± 0.2 −148.7 ± 0.4 −154.8 ± 0.8 −127.3 ± 0.3 −140.0 ± 0.6 −137.1 ± 0.5

[−692.8 ± 2.0]g −128.3 ± 0.3

S (4.0) Merli et al. (1998)

Hennig and Oppermann (1998)

S (1.0) S (3.0) S (6.0) S (4.0)

[−695.1 ± 2.0]g −689.6 ± 2.0 −693.9 ± 1.3 −695.7 ± 1.8

NdI3 Hohmann and Bommer (1941) Hennig and Oppermann (2000) selected value:

−1065.7 ± 4.3 −1036.6 ± 2.5 −1029.0 ± 0.9 −1028.9 ± 5.5 −1041.3 ± 1.0 −1036.6 ± 1.7 −1039.5 ± 1.7c −1041.5 ± 2.1d −1040.3 ± 1.0e −1041.8 ± 2.0d

−127.5 ± 0.3

−1037.1 ± 0.6f −1042.6 ± 2.0d −1040.9 ± 1.0

selected value: NdBr3 Hurtgen et al. (1980) Hennig and Oppermann (1999) selected value:

f H ◦ /kJ·mol−1

S (0.1) S (4.0)g

[−688.0 ± 2.5]g

−184.5 ± 0.6 −169.9 ± 0.2

−865.6 ± 2.6 −862.3 ± 3.1g −864.0 ± 3.0

S (0.1)

−717.1 ± 4.3 [−688.0 ± 2.5]g

−215.7 ± 0.2

−670.0 ± 4.3 −640.9 ± 2.5 −637.4 ± 1.6h −639.2 ± 4.0

S (4.0)h

−201.8 ± 0.6

a E: e.m.f. measurements, S: solution calorimetry; values in parentheses give the concentration of the solvent in mol·dm−3 ; H: high temperature equilibria. b Kondrat’ev Y.V., Thesis, University of Leningrad. Cited and recalculated by Johnson et al. (1980). c Using H ◦ from Tiﬂova (1990). 1 d Using H ◦ (interpolated) from Merli et al. (1998). 1 e Using H ◦ from Stuve (1965a). 1 f In HBr(aq); cycle based on H ◦ (Nd O (cr)). f 2 3 g Value estimated by the present authors. h In HI(aq); cycle based on H ◦ (Nd O (cr)). f 2 3

214

R.J.M. KONINGS AND A. KOVÁCS

Table B.5 The enthalpy of formation of SmX 3 (cr) at 298.15 K; H ◦1 and H ◦2 are the enthalpies of solution of Sm(cr) and SmX 3 (cr) in HCl(aq), respectively authors SmF3 Kim et al. (1977) selected value: SmCl3 Bommer and Hohmann (1941b) Machlan et al. (1955) Montgomery and Hubert (1959) Gvelesiani and Yashvili (1967) Baker et al. (1972) Morss and Fahey (1976) Khanaev et al. (1987) Hennig and Oppermann (1997)

methoda

H ◦1 /kJ·mol−1

H ◦2 /kJ·mol−1

−1669.0 ± 4.6 −1700.7 ± 5.0b

C

S (0.05) S (6.0) S (0.48) S (0.7) S (1.0) S (2.0) S (3.99) S (2.0) S (0.05)f S (4.0)

−683.7 ± 5.4 −682.6 ± 2.4 −690.1 ± 1.3 −689.5 ± 3.8

−1025.1 ± 1.8d

−151.9

−1025.8 ± 1.3e

−139.2 ± 0.2

−1025.1 ± 1.4d −1025.3 ± 3.8e −1025.3 ± 2.0

−190.2 ± 0.9

−850.5 ± 2.6g −856.9 ± 2.2 −856.3 ± 2.1c −853.4 ± 3.0

−689.6 ± 1.7

S (1.0) [−689.0 ± 2.0]h S (0.1)

−195.4 ± 0.8

S (0.05)

−237.0 ± 0.7

selected value: SmI3 Hohmann and Bommer (1941) selected value:

−1025.9 ± 1.7c

−163.2 ± 0.2 −123.4 ± 0.8 −158.5 ± 1.0

selected value: SmBr3 Hurtgen et al. (1980)

f H ◦ /kJ·mol−1

−621.5 ± 1.8c −621.5 ± 4.0

a E: e.m.f. measurements, S: solution calorimetry; values in parentheses give the concentration of the solvent in mol·dm−3 . b See main text for explanation of selected value. c Using H ◦ from Khanaev et al. (1987). 1 d Cycle based on H ◦ (Sm O (cr)). f 2 3 e Using H ◦ from Baker et al. (1972). 1 f The measurements were carried out in HClO (aq). 4 g Using H ◦ from Gvelesiani and Yashvili (1967). 1 h Estimated.

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

215

Table B.6 The enthalpy of formation of EuX 3 (cr) at 298.15 K; H ◦1 and H ◦2 are the enthalpies of solution of Eu(cr) and EuX 3 (cr) in HCl(aq), respectively authors EuCl3 Bommer and Hohmann (1941b)

methoda

Machlan et al. (1955) Burnett and Cunningham (1964), Burnett (1964) Stuve (1965b)

S (6.0) S (0.1) S (4.0)

Stubbleﬁeld et al. (1965) Fitzgibbon et al. (1972) Hennig et al. (1998)

S (6.0) S (4.0) S (4.0)

H ◦1 /kJ·mol−1

H ◦2 /kJ·mol−1 −172.2 ± 0.2

S (0.1)

−688.6 ± 2.9 −583.0 ± 2.5e

−129.3 ± 0.8

f H ◦ /kJ·mol−1 −872.3 ± 2.9b −1015.2 ± 2.9c −920.8 ± 2.6d

−143.6 ± 0.4

−914.5 ± 2.5 −936.6 ± 2.9f −936.1 ± 2.1g

−146.9 ± 0.2

−893.6 ± 2.1g −911.2 ± 2.5h −933.4 ± 2.9f −935.4 ± 3.0

−589.9 ± 2.9 −605.2 ± 2.9

selected value:

a E: e.m.f. measurements, S: solution calorimetry; values in parentheses give the concentration of the solvent in mol·dm−3 . b Using H ◦ from Burnett and Cunningham (1964). 1 c Using H ◦ from Burnett and Cunningham (1964) neglecting the effect of oxygen in the HCl(aq) solution. 1 d Using H ◦ from Stubbleﬁeld et al. (1965). 1 e Two sets of measurements with different samples of Eu(cr). f Using H ◦ from Fitzgibbon et al. (1972). 1 g Cycle based on H ◦ (Eu O (cr)). f 2 3 h Using H ◦ from Stuve (1965b). 1

Table B.7 The enthalpy of formation of GdX 3 (cr) at 298.15 K; H ◦1 and H ◦2 are the enthalpies of solution of Gd(cr) and GdX 3 (cr) in HCl(aq), respectively authors GdF3 Rudzitis and Deventer (1965) Polyachenok (1967) Kondrat’evb Kholokhova and Rezukhina (1976) Storozhenko et al. (1976) Kim et al. (1978) Johnson et al. (1980) selected value:

methoda

H ◦1 /kJ·mol−1

H ◦2 /kJ·mol−1

f H ◦ /kJ·mol−1 −1700.8 ± 1.3 −1628 −1672.2 ± 2.1 −1713.3 ± 4.6 −1646.5 ± 3.2 −1698.7 ± 7.1 −1699.3 ± 2.3 −1699.3 ± 2.3

C H S E S C C

GdCl3 Bommer and Hohmann (1941a, 1941b)

S (0.1)

−706.3 ± 2.3

−177.4 ± 0.2

Spedding and Flynn (1954) Daire (1968) Yashvili and Gvelesiani (1971)

S (0.27) S (1.0) S (6.0)

−683.6 ± 1.3 −682.8 ± 1.3 −694.5 ± 1.7

−174.1 ± 0.7

−1027.7 ± 2.3 −1005.0 ± 1.3c −1006.9 ± 1.5

continued on next page

216

R.J.M. KONINGS AND A. KOVÁCS Table B.7, continued from previous page

authors Tiﬂova et al. (1989)

methoda S (2.19)

Furkaliouk et al. (1992) Laptev et al. (1993) Merli et al. (1998)

S (1.0) E S (1.0) S (6.0) S (6.1)

H ◦1 /kJ·mol−1 −684.9 ± 0.4 [−695.2 ± 1.5]e −683.7 ± 0.7 −694.9 ± 1.0 −696.1 ± 1.1

H ◦2 /kJ·mol−1 −165.3 ± 0.2

f H ◦ /kJ·mol−1 −1006.1 ± 0.5 −1016.3 ± 1.5d −1009.8 ± 1.1 −1017.5 ± 1.3

−170.5 ± 0.7 −136.4 ± 0.7

−1018.9 ± 1.3 −1018.2 ± 1.5

selected value: GdBr3 Hurtgen et al. (1980)

S (1.0)

−214.8 ± 0.7

S (0.27) S (0.1)

[−218.4 ± 1.1] −219.9 ± 1.1

−827.0 ± 1.6c −838.2 ± 1.8d −826.3 ± 2.0f −838.2 ± 2.0

selected value: GdI3 Hohmann and Bommer (1941) Furkaliouk et al. (1992)

S (0.1) S (1.0) S (0.1)

−706.3 ± 2.3 −688.2 ± 0.8

−256.0 ± 2.5g −236.9 ± 0.3

−618.9 ± 3.4 −612.9 ± 0.9 −624.1 ± 1.1d −624.1 ± 3.0

selected value:

a E: e.m.f. measurements, S: solution calorimetry; values in parentheses give the concentration of the solvent in mol·dm−3 ; H: high temperature equilibria. b Kondrat’ev Y.V., Thesis, University of Leningrad. Cited and recalculated by Johnson et al. (1980). c Using H ◦ from Spedding and Flynn (1954). 1 d Using H ◦ from Merli et al. (1998). 1 e H ◦ estimated from the results of Merli et al. (1998). 1 f The value obtained by combining H ◦ interpolated from the results of Hurtgen et al. (1980) and H ◦ from Sped2 1 ding and Flynn (1954). g The value corrected to 298.15 K.

Table B.8 The enthalpy of formation of TbX 3 (cr) at 298.15 K; H ◦1 and H ◦2 are the enthalpies of solution of Tb(cr) and TbX 3 (cr) in HCl(aq), respectively authors TbF3 Kholokhova and Rezukhina (1976) Storozhenko et al. (1976) selected value: TbCl3 Stuve (1967a) Fitzgibbon and Holley Jr. (1968)

methoda

H ◦1 /kJ·mol−1

H ◦2 /kJ·mol−1

−1707.9 ± 5.0 −1623.3 ± 3.8 −1695.9 ± 5.0

E S

S (4.0) S (1.0)

f H ◦ /kJ·mol−1

−689.9 −701.7 ± 2.5

−167.9

−997.1 continued on next page

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

217

Table B.8, continued from previous page authors Morss (1976)

methoda S (0.89)

Bettonville et al. (1987) Furkaliouk et al. (1993) selected value:

S (1.0) S (1.0)

TbBr3 Bettonville et al. (1987)

H ◦1 /kJ·mol−1 −696.2

H ◦2 /kJ·mol−1 −181.5

f H ◦ /kJ·mol−1 −1008.6b −1013.9c −1009.2d −998.2e

−697.0 ± 1.2 −686.0 ± 0.6

−1010.6 ± 3.0

S (1.0)

−697.0 ± 1.2

−216.0 ± 1.5

−842.1 ± 2.0 −841.5f −846.8 ± 3.0c −843.5 ± 3.0

S (1.0) S (1.0)

−682.7 ± 0.4 −686.0 ± 0.6

−240.7 ± 0.3 −240.7 ± 0.3

−608.1 ± 0.5 −611.4 ± 0.7 −621.8f −627.1 ± 1.2c −622.4 ± 2.5d −623.8 ± 3.0

selected value: TbI3 Furkaliouk (1993) Furkaliouk et al. (1993)

selected value:

a E: e.m.f. measurements, S: solution calorimetry; values in parentheses give the concentration of the solvent in mol·dm−3 . b Quoted in Morss (1976). c Using H ◦ from Fitzgibbon and Holley Jr. (1968). 1 d Using H ◦ from Bettonville et al. (1987). 1 e Using H ◦ from Furkaliouk et al. (1993). 1 f Using H ◦ from Morss (1976). 1

Table B.9 The enthalpy of formation of DyX 3 (cr) at 298.15 K; H ◦1 and H ◦2 are the enthalpies of solution of Dy(cr) and DyX 3 (cr) in HCl(aq), respectively authors DyF3 Storozhenko et al. (1976) Kim et al. (1980) Johnson et al. (1980) selected value: DyCl3 Bommer and Hohmann (1941a, 1941b) Morss (1976)c

methoda

H ◦1 /kJ·mol−1

H ◦2 /kJ·mol−1

−1640.2 ± 4.5 −1678 ± 8 −1692.0 ± 1.9 −1692.0 ± 1.9

S C C

S (0.1)b S (4.0)

f H ◦ /kJ·mol−1

−695.5 ± 0.2 −692.4

−197.9 ± 0.4 −180.4

−996.4 ± 0.5 −987.0 −989.9 ± 3.0d continued on next page

218

R.J.M. KONINGS AND A. KOVÁCS

Table B.9, continued from previous page H ◦1 /kJ·mol−1 −695.3 ± 2.9 −691 ± 9 −704.2 ± 0.6 −701.0 ± 0.6 −706.5 ± 0.4

H ◦2 /kJ·mol−1

S (4.0)

−699.4 ± 1.3

−180.1 ± 0.2

S (0.1)b S (1.0) S (0.1) S (0.1) S (1.0)

−694.0 ± 0.2

authors Huber Jr. et al. (1971) Morss and Fahey (1976) Monaenkova et al. (1989) Tiﬂova (1990)

methoda S (4.0) S (4.0) S (2.19) S (1.07) S (4.01)

Cordfunke et al. (1996)

−180.4 ± 1.1 −190.7 ± 0.2 −198.8 ± 0.3 −177.2 ± 0.5

selected value: DyBr3 Bommer and Hohmann (1941a) Hurtgen et al. (1980)

Cordfunke and Booij (1997)

−218.9 ± 0.2 −223.2 ± 1.4 −223.2 ± 1.4 [−224.9 ± 0.4]i

selected value: DyI3 Hohmann and Bommer (1941) Morss and Spence (1992) Cordfunke and Booij (1997) Leonidov and Furkalyuk (1999) selected value:

S (0.1)b S (1.0) S (1.0) S (4.0)

−694.8 ± 0.2 −691 ± 9

−256.7 ± 1.0 −242 ± 8 [−248.9 ± 0.4]i −229.0 ± 0.6

f H ◦ /kJ·mol−1 −985.6 ± 9.1 −999.9 ± 0.7 −995.0 ± 0.7 −1004.4 ± 0.7 −993.1 ± 3.0d −992.9 ± 3.1e −994.4 ± 1.3 −990.0 ± 3.0e −993.1 ± 3.0

−840.2 ± 0.7f −834.4 ± 1.5g −838.3 ± 1.7h −835.0 ± 1.5 −834.3 ± 2.2h −834.3 ± 3.0 −606.7 ± 1.0 −615.1 ± 12.0 −619.3 ± 1.8 −616.7 ± 2.1h −621.7 ± 1.4j −616.7 ± 3.0

a E: e.m.f. measurements, S: solution calorimetry; values in parentheses give the concentration of the solvent in mol·dm−3 . b The measurements were carried out at 294 K. c Cited in Morss (1976). d Using H ◦ from Huber Jr. et al. (1971). 1 e Cycle based on H ◦ (Dy O (cr)). f 2 3 f Using H ◦ from Tiﬂova (1990). 1 g Using H ◦ from Bommer and Hohmann (1941a). 1 h Cycle based on H ◦ (CeCl (cr)). f 3 i Estimated from Cordfunke and Booij (1997). j Using H ◦ from Cordfunke and Booij (1997). 1

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

219

Table B.10 The enthalpy of formation of HoX 3 (cr) at 298.15 K; H ◦1 and H ◦2 are the enthalpies of solution of Ho(cr) and HoX 3 (cr) in HCl(aq), respectively authors HoF3 Rudzitis and Deventer (1965) Kim and Oishi (1979) Johnson et al. (1980) selected value: HoCl3 Bommer and Hohmann (1941a) Stuve (1967a) Morss (1976)b

methoda

H ◦1 /kJ·mol−1

H ◦2 /kJ·mol−1

f H ◦ /kJ·mol−1 −1700.8 ± 4.2 −1698 ± 6 −1697.8 ± 2.3 −1697.8 ± 2.3

C C C

S (0.1) S (4.0) S (0.87)

−686.2 −710.5 ± 7.1 −698.3

−209.2 −180.5 ± 0.3 −202.3

−975.8 −1005.1 ± 7.1 −980.8 −997.4d

S (1.0)c S (1.07)

−705.9 ± 1.9 −704.5 ± 2.2

−199.2 ± 0.8

−998.0 ± 2.4 −997.7 ± 2.5

HoBr3 Bettonville et al. (1987) selected value:

S (1.0)d

−705.9 ± 2.4

−221.9 ± 1.2

−842.1 ± 2.7 −842.1 ± 3.0

HoI3 Bommer and Hohmann (1941a) Lezhava (1992) selected value:

S (0.1) S

−686.2

−259.4 −255.1 ± 1.2

−596.4 −622.9 ± 3.2 −622.9 ± 3.0

Bettonville et al. (1987) Lezhava (1992) selected value:

a E: e.m.f. measurements, S: solution calorimetry; values in parentheses give the concentration of the solvent in mol·dm−3 . b Quoted in by Morss (1976). c Two different samples of Ho(cr) were used. d Using H ◦ from Bettonville et al. (1987). 1

Table B.11 The enthalpy of formation of ErX 3 (cr) at 298.15 K; H ◦1 and H ◦2 are the enthalpies of solution of Er(cr) and ErX 3 (cr) in HCl(aq), respectively authors ErF3 Polyachenok (1967) Kondrat’evb Kim et al. (1979) Johnson et al. (1980) selected value:

methoda

H ◦1 /kJ·mol−1

H ◦2 /kJ·mol−1

−1582 −1635.0 ± 8.4 −1669 ± 6 −1693.6 ± 1.9 −1693.6 ± 1.9

H S C C

ErCl3 Bommer and Hohmann (1941a, 1941b) Spedding and Flynn (1954) Montgomery and Stuve (1961)

S (0.1) S (1.42) S (1.4)

Gamanovich and Glybin (1974)c Fuger et al. (1980)

S (2.03) S (1.43)

f H ◦ /kJ·mol−1

−680.1 ± 3.1 −661.4 ± 0.9

−705.6 ± 1.4

−207.3 ± 0.2 −193.3 ± 0.4 −201.9 ± 0.9

−971.6 ± 3.1 −958.9 ± 1.0 −994.5 ± 1.7c −994.3 ± 2.8d

−201.7 ± 1.2 −201.7 ± 0.2 −994.6 ± 1.4 continued on next page

220

R.J.M. KONINGS AND A. KOVÁCS Table B.11, continued from previous page

authors Tiﬂova (1990)e Furkaliouk et al. (1993) Merli et al. (1998) selected value: ErBr3 Hurtgen et al. (1980) selected value: ErI3 Bommer and Hohmann (1941a) Furkaliouk and Cordfunke (1996)

methoda S (2.19) S (2.19) S (1.0) S (6.0)

H ◦1 /kJ·mol−1 −681.9 ± 0.7 −682.9 ± 1.8 −681.8 ± 0.7 −707.0 ± 1.2

H ◦2 /kJ·mol−1 −197.3 ± 0.2 −197.3 ± 0.2

f H ◦ /kJ·mol−1 −971.1 ± 0.8 −972.1 ± 1.8 −994.4 ± 2.0

S (1.0)

[−705.0 ± 3.0]f

−226.0 ± 0.5

−837.1 ± 3.0 −837.1 ± 3.0

S (0.1) S (1.0)

−680.1 ± 3.1 −681.8 ± 0.7 [−705.0 ± 3.0]f

−261.1 ± 0.6 −252.1 ± 0.2

−587.6 ± 3.2 −595.8 ± 0.7 −619.0 ± 3.0f −619.0 ± 3.0

selected value:

a E: e.m.f. measurements, S: solution calorimetry; values in parentheses give the concentration of the solvent in mol·dm−3 ; H: high temperature equilibria. b Kondrat’ev Y.V., Thesis, University of Leningrad. Cited and recalculated by Johnson et al. (1980). c Using H ◦ from Fuger et al. (1980). 1 d Based on the enthalpy of solution of Er O . 2 3 e Two sets of measurements with different samples of Er(cr). f The value estimated from the results of Fuger et al. (1980) and Merli et al. (1998).

Table B.12 The enthalpy of formation of TmX 3 (cr) at 298.15 K; H ◦1 and H ◦2 are the enthalpies of solution of Tm(cr) and TmX 3 (cr) in HCl(aq), respectively authors TmF3 Kim et al. (1980) selected value: TmCl3 Bommer and Hohmann (1941a, 1941b) Stuve (1967b) Morss (1976)c Lezhava (1992)d selected value: TmI3 Hohmann and Bommer (1941) Lezhava (1992) selected value:

methoda

H ◦1 /kJ·mol−1

H ◦2 /kJ·mol−1

−1656 ± 7 −1693.7 ± 5.0b

C

S (0.1) S (4.0) S (1.07)

S (0.1) S (H2 O)

f H ◦ /kJ·mol−1

−675.7 ± 0.4 −698.0 ± 1.3 −705.7 −709.3 ± 0.8

−212.9 ± 0.1 −186.6 ± 0.9 −205.8 −203.3 ± 0.4

−961.6 ± 0.5 −986.5 ± 1.6 −993.8 −998.7 ± 0.9 −996.3 ± 2.5

−675.7 ± 0.4

−261.9 −261.8 ± 1.8

−583.4 −619.7 ± 3.5e −619.7 ± 3.5

a E: e.m.f. measurements, S: solution calorimetry; values in parentheses give the concentration of the solvent in mol·dm−3 . b See main text for explanation. c Quoted in Morss (1976). d Two sets of measurements with different samples of Tm(cr). e Based on H ◦ (Tm3+ , aq) (Cordfunke and Konings, 2001a). f

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

221

Table B.13 The enthalpy of formation of YbX 3 (cr) at 298.15 K; H ◦1 and H ◦2 are the enthalpies of solution of Yb(cr) and YbX 3 (cr) in HCl(aq), respectively authors YbF3 Kim et al. (1978) selected value: YbCl3 Bommer and Hohmann (1941a) Machlan et al. (1955) Stuve (1967b) Bettonville et al. (1987) selected value: YbBr3 Burgess and Kijowski (1981) Bettonville et al. (1987)

methoda

H ◦1 /kJ·mol−1

H ◦2 /kJ·mol−1

f H ◦ /kJ·mol−1 −1569.8 ± 7.1 −1655.1 ± 3.0b

C

S (0.05) S (6.0) S (4.0) S (6.0)

S (H2 O) S (6.0) S (1.0)

−671.7 ± 2.8 −664.9 ± 1.1

−664.9 ± 1.1 [−663.0 ± 3.0]d

−213.2 ± 0.2 −165.7 ± 1.3 −187.2 ± 0.8

−959.4 ± 1.7c −959.5 ± 2.9 −959.5 ± 3.0 −787.2 ± 4.4e −792.6 ± 1.8 −791.9 ± 3.4 −791.9 ± 5.0

−253.3 ± 3.2 −199.9 ± 1.4 −229.8 ± 1.5

selected value:

a E: e.m.f. measurements, S: solution calorimetry; values in parentheses give the concentration of the solvent in mol·dm−3 . b See main text for explanation. c Using H ◦ from Bettonville et al. (1987). 1 d Estimated by Cordfunke and Konings (2001b). e Based on H ◦ (Yb3+ , aq) (Cordfunke and Konings, 2001a). f

Table B.14 The enthalpy of formation of LuX 3 (cr) at 298.15 K; H ◦1 and H ◦2 are the enthalpies of solution of Lu(cr) and LuX 3 (cr) in HCl(aq), respectively authors LuF3 Kholokhova and Rezukhina (1976) selected value:

methoda

H ◦2 /kJ·mol−1

S (0.1) S (0.89)

Tiﬂova (1990)

S (2.19)

Furkaliouk et al. (1993) Merli et al. (1998)

S (1.0) S (1.0) S (3.0) S (6.0)

f H ◦ /kJ·mol−1 −1700.8 ± 5.0 −1679.9 ± 5.0b

E

LuCl3 Bommer and Hohmann (1941a)b Morss (1976)c

selected value:

H ◦1 /kJ·mol−1

−670.7 −700.0

−694.9 ± 1.0 [−702.7 ± 2.5]f −687.7 ± 0.5 −702.3 ± 2.2 −703.1 ± 1.3 −703.9 ± 2.2

−214.6 −208.1

−954.9 −985.6 −973.3d −987.9e −981.9 ± 1.1 −989.7 ± 2.6

−199.5 ± 0.3

−210.5 ± 0.70 −175.9 ± 0.90

−984.9 ± 2.3

−988.2 ± 3.0 −987.1 ± 2.5 continued on next page

222

R.J.M. KONINGS AND A. KOVÁCS Table B.14, continued from previous page

authors LuI3 Hohmann and Bommer (1941)b Furkaliouk and Cordfunke (1996)

methoda S (0.1) S (1.0)

H ◦1 /kJ·mol−1

H ◦2 /kJ·mol−1

−670.7 −685.0 ± 0.5

−279.8 −263.3 ± 0.4

selected value:

f H ◦ /kJ·mol−1 −559.5 −587.8 ± 0.7 −605.1 ± 2.2e −605.1 ± 2.2

a E: e.m.f. measurements, S: solution calorimetry; values in parentheses give the concentration of the solvent in mol·dm−3 . b See main text for explanation. c Quoted by Morss (1976). d Using H ◦ from Furkaliouk and Cordfunke (1996). 1 e Using H ◦ from Merli et al. (1998). 1 f Estimated value.

Appendix C. Experimental data for the liquid trihalides Table C.1 Experimental results for the enthalpy of fusion and heat capacity of the liquid lanthanide trichlorides fus H ◦ /kJ·mol−1

Cp (liq) /J·K−1 ·mol−1

LaCl3 Dworkin and Bredig (1963a) Savin et al. (1979) Gaune-Escard et al. (1994) selected value:

54.4 31.0 ± 2.1 55.7 55.0

157.7 349.4

CeCl3 Walden and Smith (1961) Savin and Mikhailova (1981) Gaune-Escard et al. (1994) selected value:

53.6 33.5 55.5 53.6

161.05

PrCl3 Dworkin and Bredig (1963a) Savin et al. (1979) Gaune-Escard et al. (1994) selected value:

50.6 28.9 ± 2.1 49.1 49.9

133.9 179.9 155.28 155.3

NdCl3 Dworkin and Bredig (1963a) Savin and Mikhailova (1981) Gaune-Escard et al. (1994) selected value:

50.2 33.5 48.1 49.2

146.4

SmCl3 Rycerz and Gaune-Escard (2002a) selected value:

47.6 47.6

compound

157.7

161.05

149.53 149.5 145.26 145.26 continued on next page

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

223

Table C.1, continued from previous page compound EuCl3 Rycerz and Gaune-Escard (2002b) selected value:

fus H ◦ /kJ·mol−1

Cp (liq) /J·K−1 ·mol−1

45.0 45.0

155.96 149.5

GdCl3 Dworkin and Bredig (1963b) Dworkin and Bredig (1971) Goryushkin et al. (1990) Gaune-Escard et al. (1994) selected value:

40.2 40.6 60.3 ± 12 40.6 40.6

141.0 139.52

DyCl3 Dworkin and Bredig (1971) Goryushkin et al. (1990) Gaune-Escard et al. (1996) selected value:

25.5 36.5 ± 7.3 27.6 25.5

144.77

TbCl3 Dworkin and Bredig (1963b) Goryushkin et al. (1990) Rycerz and Gaune-Escard (1999b) selected value:

19.5 31.6 ± 6.3 20.8 19.5

144.47

HoCl3 Dworkin and Bredig (1963b) Dworkin and Bredig (1971) Goryushkin et al. (1990) selected value:

29.3 32.6 37.9 ± 7.6 32.6

147.7 148.66

ErCl3 Dworkin and Bredig (1963b) Gaune-Escard et al. (1996) Goryushkin et al. (1990) selected value:

32.6 31.1 38.5 ± 7.7

141.0

TmCl3 Goryushkin et al. (1990) Gaune-Escard et al. (1996) selected value:

46.9 ± 9.4 35.6 35.6

YbCl3 Goryushkin et al. (1990) selected value:

58.1 ± 11.6 37.6

LuCl3 Goryushkin et al. (1990) selected value:

59.3 ± 11.9 39.5

139.89 139.7

159.43 144.77

139.27 144.77

148.66

141.0

141.0

224

Appendix D. Molecular parameters of the lanthanide trihalides Table D.1 Experimental structural parameters and vibrational frequencies of the lanthanide triﬂuorides; bond distances in pm, bond angles in degrees, frequencies in cm−1 authors

method

symmetry

r(Ln–X)

(X–Ln–X)

vibrational frequencies ν1 (A1 )

LaF3 Akishin et al. (1959) Hargittai (1999) Wesley and DeKock (1971)

CeF3 Wesley and DeKock (1971)

Hastie et al. (1975)

PrF3 Zasorin (1988) Wesley and DeKock (1971)

Lesiecki et al. (1972)

D3h D3h D3h D3h C3v C3v C3v C3v

IR/matrix (Ar) IR/matrix (Kr) IR/matrix (N2 ) IR/matrix (Ne) IR/matrix (Ar) IR/matrix (N2 ) IR/gas (estimated)

D3h D3h D3h C3v C3v C3v C3v

ED/gas (rg ) ED/gas (re ) IR/matrix (Ar) IR/matrix (Kr) IR/matrix (N2 ) Raman/matrix (Ar) IR/matrix (Ar)

C3v C3v D3h D3h D3h D3h D3h

ν3 (E)

ν4 (E)

222(3) 213(6) 84

527.9 513.0 490 540(10)

84 81 83 94 82(10) 86

536.9 521.5 506 549(8) 209.1(3) 205.6(5)

86 78 94 82 80(15)

478 474 457 496.6 479.0 459 510(10) 483 479 465 505.3 488.3 468 519(8)

120 116 130 121.1 112 125(10)

116 134 121 115(15)

102.6(28) 105.0(15) 542 538

86 86

526 542

86

458 99 455 488 118 458 99 458 99 continued on next page

R.J.M. KONINGS AND A. KOVÁCS

Hastie et al. (1975)

ED/gas (ra ) ED/gas (rα ) IR/matrix (Ar) IR/matrix (Kr) IR/matrix (N2 ) IR/matrix (Ne) IR/matrix (Ar) IR/matrix (N2 ) IR/gas (estimated)

ν2 (A1 )

Table D.1, continued from previous page authors

method

symmetry

r(Ln–X)

(X–Ln–X)

vibrational frequencies ν1 (A1 )

Hastie et al. (1975)

SmF3 Wesley and DeKock (1971)

EuF3 Wesley and DeKock (1971)

Hastie et al. (1975)

GdF3 Zasorin (1988) Hastie et al. (1975)

TbF3 Hauge et al. (1971)

ν2 (A1 ) 86

ν3 (E)

IR/matrix (Ar) IR/matrix (Kr) IR/matrix (N2 ) IR/matrix (Ne) IR/matrix (Ar) IR/matrix (N2 ) IR/gas (estimated)

D3h D3h D3h C3v C3v C3v C3v

IR/matrix (Ar) IR/matrix (Kr) IR/matrix (N2 )

D3h D3h D3h

92

508 504 491

123

IR/matrix (Ar) IR/matrix (Kr) IR/matrix (N2 ) IR/matrix (Ne) IR/matrix (Ar) IR/matrix (N2 ) IR/gas (estimated)

D3h D3h D3h C3v C3v C3v C3v

94

124

133 127 120 120(10)

ED/gas (rg ) ED/gas (re ) IR/matrix (Ne) IR/matrix (Ar) IR/matrix (N2 ) IR/gas (estimated)

C3v C3v C3v C3v C3v C3v

138 133 143 130(10)

IR/matrix (Ne) IR/matrix (Ar) IR/matrix (N2 )

C3v C3v C3v

544.9 529.7 505 557(10)

205.3(3) 201.6(6)

86 81 87 103 80(15)

502 499 482 521.4 503.7 483 535(10)

ν4 (E)

557.5 542.4 532 572(10)

89 94.0 101 90(15)

511 507 502 529.5 511.7 504 544(10)

560.2 544.7 532 583(10)

94 100 116 95(15)

537.3 519.2 500 552(10)

118 123 121 119 124 115(15)

108.4(24) 109.9(23)

566.7 551.1

225

540.1 523.1 509 continued on next page

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

NdF3 Wesley and DeKock (1971)

226

Table D.1, continued from previous page authors

method

symmetry

r(Ln–X)

(X–Ln–X)

vibrational frequencies ν1 (A1 )

DyF3 Bencze et al. (1996)

Hauge et al. (1971)

ErF3 Bencze et al. (1996) TmF3 Bencze et al. (1996) YbF3 Hauge et al. (1971)

LuF3 Hauge et al. (1971)

554.4 540.2

ν3 (E)

ν4 (E)

IR/matrix (Ar) IR/matrix (N2)

C3v C3v

ED/gas (rg ) ED/gas (re ) IR/matrix (Ne) IR/matrix (Ar) IR/matrix (N2 )

C3v C3v C3v C3v C3v

IR/matrix (Ar) IR/matrix (N2)

C3v C3v

560.7 546.0

539.4 524

IR/matrix (Ar) IR/matrix (N2)

C3v C3v

566.2 547

544.8 529

IR/matrix (Ne) IR/matrix (Ar) IR/matrix (N2 )

C3v C3v C3v

584.1 568.5

100

564.7 546.4 526

144

IR/matrix (Ne) IR/matrix (Ar) IR/matrix (N2 )

C3v C3v C3v

585.4 569.6

101 112 121

570.5 552.2 530

150 144 149

200.7(3) 197.8(10)

531.6 513

105.8(24) 108.2(32) 572.4 556.7

94 104 124

554.0 535.6 516

122 119 143

R.J.M. KONINGS AND A. KOVÁCS

HoF3 Zasorin (1988)

ν2 (A1 )

Table D.2 Experimental structural parameters and vibrational frequencies of the lanthanide trichlorides; bond distances in pm, bond angles in degrees, frequencies in cm−1 authors

method

symmetry

r(Ln–X)

(X–Ln–X)

vibrational frequencies ν1 (A1 )

Spiridonov et al. (1990) Girichev (2002) Selivanov et al. (1973) Perov et al. (1975) Kovács and Konings (1997a) CeCl3 Krasnov (1979) Kovács and Konings (1997b) PrCl3 Zasorin (1988) Selivanov et al. (1973) NdCl3 Selivanov et al. (1973) Wells Jr. et al. (1977) Feltrin and Cesaro (1996) Kovács and Konings (1997b) SmCl3 Kovács and Konings (1997b) GdCl3 Zasorin (1988) Giricheva et al. (2000d) Selivanov et al. (1973) Perov et al. (1975) Kovács and Konings (1997b)

ED/gas (rg ) ED/gas (re ) ED/gas (re ) ED/gas (rg ) IR/gas IR/matrix (Xe) IR/gas

C3v C3v C3v D3h

C3v

ED/gas (rg ) ED/gas (re ) IR/gas

C3v C3v

256.9(10)

255.4(5) 251.0(9)

ν4 (E)

52 59

316 300 317

58

321

74

111.6(20)

112.5(15) 114.3(20) 320

349

D3h D3h

IR/gasa ED/gas (rg ) ED/gas (re ) ED/gas (rg ) IR/gas IR/matrix (Xe) IR/gasa

ν3 (E)

112.8(17) 115.4(20) 116.5(3) 116.7(12)

D3h

ED/gas IR/gasa

IR/gas IR/gas IR/matrix (Ar) IR/gasa

258.9(5) 253.8(9) 256.0(6) 258.9(6)

ν2 (A1 )

C3v C3v D3h D3h

248.8(5) 244.5(7) 247.4(5)

60

324 301 328.3 327

61

331

177

120

112.3(12) 113.5(21) 117.0(11) 53 64

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

LaCl3 Zasorin (1988)

326 318 82 337 continued on next page 227

228

Table D.2, continued from previous page authors

method

symmetry

r(Ln–X)

(X–Ln–X)

vibrational frequencies ν1 (A1 )

TbCl3 Zasorin (1988)

Kovács and Konings (1997b) HoCl3 Zasorin (1988) Loktyushina et al. (1987) ErCl3 Giricheva et al. (2000c) Perov et al. (1975) TmCl3 Giricheva et al. (2000a) Feltrin and Cesaro (1996) LuCl3 Zasorin (1988) Giricheva et al. (2000b) Perov et al. (1975)

ED/gas (rg ) IR/matrix (Ar) Raman/matrix (Xe) IR/matrix (Xe) IR/gasa

C3v C3v D3h

247.6(5) 243.8(8) 247.1(5)

ν4 (E)

111.2(15) 112.9(19) 115.5(11)

246.1(8) 340.2

D3h 318 65

ED/gas (rg ) ED/gas (re ) IR/matrix (Ar)

C3v C3v

ED/gas (rg ) ED/gas (re ) IR/matrix (Xe)

C3v C3v D3h

243.0(5) 239.3(5)

ED/gas (rg ) IR/matrix (Ar)

D3h D3h

242.2(6)

ED/gas (rg ) ED/gas (re ) ED/gas (rg ) ED/gas (rα ) IR/matrix (Xe)

ν3 (E)

R.J.M. KONINGS AND A. KOVÁCS

Girichev (2002) DyCl3 Hargittai (2000) Feltrin and Cesaro (1996) Groen (2002)

ED/gas (rg ) ED/gas (re ) ED/gas (rg )

ν2 (A1 )

246.2(5) 242.5(9)

324.2 340

111.7(15) 112.6(19) 340

D3h D3h

a Re-interpretation of the gas-phase spectra presented by Kovács et al. (1995).

112.3(12) 328 116.2(14) 346.1

241.7(6) 237.4(10) 240.3(5) 236.7(6)

111.5(20) 114.5(24) 117.9(13) 120.2(15) 60

331

88

Table D.3 Experimental structural parameters and vibrational frequencies of the lanthanide tribromides; bond distances in pm, bond angles in degrees, frequencies in cm−1 authors

method

symmetry

r(Ln–X)

(X–Ln–X)

vibrational frequencies ν1 (A1 )

Kovács and Konings (1997a) PrBr3 Girichev et al. (2002) NdBr3 Zakharov et al. (2003) Wells Jr. et al. (1977) GdBr3 Zasorin (1988) Loktyushina and Mal’tsev (1984) DyBr3 Hargittai (2000) Feltrin and Cesaro (1996) Groen (2002)

HoBr3 Girichev et al. (2002) Loktyushina et al. (1987) ErBr3 Zakharov et al. (2001) TmBr3 Feltrin and Cesaro (1996)

ED/gas (rg ) ED/gas (rg ) ED/gas (re ) IR/gas

C3v C3v C3v

ED/gas (rg )

D3h

269.6(6)

114.7(10)

ED/gas (rg ) IR/gas

D3h D3h

267.5(6)

115.0(12)

ED/gas (rg ) ED/gas (re ) IR/matrix (Xe) IR/matrix (Ar)

C3v C3v

264.1(4) 259.0(9)

ED/gas (rg ) IR/matrix (Ar) IR/gas IR/matrix (Kr) IR/matrix (Xe) Raman/matrix (Kr) Raman/matrix (Xe)

274.1(5) 274.2(4) 269.3(10)

ν2 (A1 )

ν3 (E)

ν4 (E)

115.5(20) 114.3(17) 115.0(23) ca.30

220

120

232

188

80

113.7(20) 115.2(23) 255 238

260.9(8) D3h 44

210 202

ED/gas (rg ) IR/matrix (Ar)

D3h

ED/gas (rg ) ED/gas (re )

D3h D3h

IR/matrix (Ar)

D3h

259.5(6)

243.1 243 237.2 229.4 237 227

47

115.3(11) 241.5

258.2(6) 256.1(9)

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

LaBr3 Giricheva et al. (1977) Zasorin (1988)

116.0(14) 120(2)

229

249.9 continued on next page

230

Table D.3, continued from previous page authors

method

symmetry

r(Ln–X)

(X–Ln–X)

vibrational frequencies ν1 (A1 )

LuBr3 Zasorin (1988) Loktyushina and Mal’tsev (1984)

ED/gas (rg ) ED/gas (re ) IR/matrix (Xe) IR/matrix (Ar)

C3v C3v

255.7(4) 251.6(8)

ν2 (A1 )

ν3 (E)

ν4 (E)

115.0(11) 117.2(17) 231 245

authors

method

symmetry

r(Ln–X)

(X–Ln–X)

vibrational frequencies ν1 (A1 )

LaI3 Hargittai (1999) Kovács and Konings (1997a) CeI3 Molnár et al. (1996) PrI3 Zasorin (1988) NdI3 Zasorin (1988) Ezhov et al. (2000) Wells Jr. et al. (1977)

ED/gas (rα ) IR/gas

ν2 (A1 )

ν3 (E)

ν4 (E)

286(3)

ED/gas (rg ) IR/gas

D3h D3h

294.8(9)

ED/gas (rg ) ED/gas (re )

C3v C3v

290.1(4) 285.4(7)

113.4(13) 113.7(19)

ED/gas (rg ) ED/gas (re ) ED/gas (rg ) ED/gas (re ) IR/gas

C3v C3v D3h D3h D3h

287.9(4) 283.5(8) 287.3(4) 286.6(5)

113.8(11) 113.9(16) 118.6(11) 118(2) 195

ca.25

191

ca.25a

191(10)

98

141 72 continued on next page

R.J.M. KONINGS AND A. KOVÁCS

Table D.4 Experimental structural parameters and vibrational frequencies of the lanthanide triiodides; bond distances in pm, bond angles in degrees, frequencies in cm−1

authors

method

symmetry

r(Ln–X)

(X–Ln–X)

vibrational frequencies ν1 (A1 )

GdI3 Zasorin (1988) Loktyushina and Mal’tsev (1984) DyI3 Feltrin and Cesaro (1996) Groen (2002)

HoI3 Loktyushina and Mal’tsev (1984) TmI3 Feltrin and Cesaro (1996) LuI3 Zasorin (1988) Loktyushina and Mal’tsev (1984)

ED/gas (rg ) ED/gas (re ) IR/matrix (Xe)

C3v

IR/matrix (Ar) IR/gas IR/matrix (Xe) Raman/matrix (Xe)

D3h

284.0(4) 279.4(7)

ν3 (E)

115.4(13) 115.5(16) 183.5

32 157

IR/matrix (Xe) IR/matrix (Ar)

189.5 195 185 184 185 196.5

IR/matrix (Ar)

D3h

ED/gas (rg ) ED/gas (re ) IR/matrix (Ar)

C3v C3v

a Band not assigned in Molnár et al. (1996).

ν2 (A1 )

198.9 276.8(3) 273.5(6)

115.6(6) 116.6(10) 198

ν4 (E)

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

Table D.4, continued from previous page

231

232

R.J.M. KONINGS AND A. KOVÁCS

Table D.5 Experimental and computed geometrical parameters of selected Ln2 X 6 dimers; bond distances in pm, bond angles in degrees Geometrya

Ln2 X 6 La2 F6 b Dy2 F6 b La2 Cl6 b Ce2 Cl6 c Pr2 Cl6 c Nd2 Cl6 c Dy2 Cl6 d Dy2 Cl6 b Er2 Cl6 e Lu2 Cl6 f La2 Br6 b Ce2 Br6 i Dy2 Br6 d Dy2 Br6 b Er2 Br6 g La2 I6 b Ce2 I6 h Ce2 I6 i Dy2 I6 b

rr 236.2 221.9 281.4 277.5 275.4 273.5 268.0(10) 266.4 265(4) 258.9(24) 297.1 301.3 281.1(9) 282.0 275.8(20) 318.8 320.7(23.8) 322.0 303.6

rt 212.6 200.8 258.4 257.0 254.9 253.0 244.9(10) 245.2 244.4(5) 236.6(5) 273.9 278.1 259.4(8) 260.4 258.8(6) 296.1 294.8(9) 299.3 282.4

αr1 70.6 73.0 80.6 82.7 83.4 81.1 84.1(34) 83.6 84(10) 84(2) 83.7 83.9 91.7(17) 87.0 81(7) 87.6 88.5 90.8

αr2 109.4 107.0 99.4 – – 99.4

αt 116.7 117.2 117.0 116.5 116.3 116.3

96.4

116.7 117(5) 119(7) 115.0 117.0

96.3 96.1 93.0 92.4

115.7 116(7) 114.5

91.5 89.2

116.7 115.3

a r , α and α indicate the geometrical parameters of the ring, while r and α the terminal ones of the dimer (cf. r r1 t t r2 ﬁg. 36). b Computed by Kovács (2000). c Computed by Kapala et al. (2002). d From ED investigations by Hargittai (2000). e r parameters by Giricheva et al. (2000c). g f r parameters by Giricheva et al. (2000b). α g r parameters by Zakharov et al. (2001). g h r parameters by Molnár et al. (1996). g i Computed by Kovács (1999).

Au B1u B2u

B3u

Ag

B1g B2g B3g

La2 F6 a 64 71 302 41 163 518 120 386 520 98 152 352 534 55 511 73 301 113

Dy2 F6 a 58 67 331 40 177 540 122 406 547 100 156 390 559 53 534 71 334 124

La2 Cl6 a 29 33 226 14 88 333 64 230 317 54 97 234 328 32 329 42 190 65

a Computed by Kovács (1999, 2000). b Computed by Kapala et al. (2002).

Ce2 Cl6 b 32 32 233 12 91 330 64 236 312 53 91 238 323 44 327 42 198 74

Pr2 Cl6 b 34 35 237 10 91 334 65 236 315 54 92 241 326 45 330 45 199 75

Nd2 Cl6 b 34 38 240 12 92 336 66 236 317 55 94 243 328 47 332 46 200 76

Dy2 Cl6 a 30 38 244 12 94 345 71 237 331 58 100 253 341 36 341 48 200 70

La2 Br6 a 18 23 161 7 51 240 42 151 214 34 72 151 226 23 236 32 131 36

Ce2 Br6 a 19 28 164 9 53 239 43 151 212 34 72 152 223 25 236 37 136 38

Dy2 Br6 a 21 29 173 8 55 243 47 154 220 38 75 162 230 27 240 38 136 39

La2 I6 a 14 18 137 5 34 195 31 110 171 24 53 112 182 19 193 25 108 24

Ce2 I6 a 14 21 140 5 36 195 31 110 169 24 54 113 180 20 193 28 112 26

Dy2 I6 a 16 23 144 5 39 195 34 113 171 27 57 120 181 23 193 31 110 27

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

Table D.6 Computed vibrational frequencies of selected Ln2 X 6 compounds, in cm−1 a

233

234

R.J.M. KONINGS AND A. KOVÁCS

Appendix E. The enthalpies of sublimation of the lanthanide trihalides Table E.1 Enthalpy of sublimation of the gaseous lanthanide triﬂuorides methoda

T /K

sub H ◦ (298.15 K)/kJ·mol−1

K M TE L T K M M K

1200–1405 1303–1416 1333–1532 1343–1640 1378–1573 1097–1222 1221–1412 1326–1644 1419–1661

446.9 ± 0.8 448.5 ± 0.9 448.5 ± 1.0 440.9 ± 0.2 442.0 ± 0.7 359.5 ± 2.4 447.7 ± 0.6 441.0 443.0 ± 0.7 444.8 ± 3.0

K TE M M M

1373–1658 1333–1532 1301–1485 1262–1586 1343–1476

439.4 ± 2.0 437.8 ± 0.4 411.6 437.6 447.5 438.3 ± 2.0

TE M K M

1335–1465 1327–1491 1430–1586 1424–1584

435.8 ± 0.7 419.1 435.2 ± 0.1 435.4 ± 0.3 435.5 ± 2.0

NdF3 Suvorov et al. (1966) Zmbov and Margrave (1966)b McCreary and Thorn (1974a) selected value:

TE M M

1334–1490 1383–1520 1325–1470

450.7 ± 1.1 433.2 ± 0.7 445.8 433.2 ± 5.0

PmF3 Gibson and Haire (1989) selected value:

Mc

1373–1553

443 430 ± 15

SmF3 Zmbov and Margrave (1968) selected value:

M

1362–1506

428.7 429 ± 10

EuF3 Zmbov and Margrave (1968) selected value:

M

1382–1522

436.9 437 ± 10

GdF3 Zmbov and Margrave (1968) McCreary and Thorn (1973b) selected value:

M M

1391–1527 1465d

authors LaF3 Kent et al. (1966)b Suvorov et al. (1966) Mar and Searcy (1967) Suvorov and Novikov (1968) Skinner and Searcy (1971) Roberts and Searcy (1972) Petzel et al. (1992) selected value: CeF3 Lim and Searcy (1966) Suvorov et al. (1966) Zmbov and Margrave (1968) Roberts and Searcy (1972) McCreary and Thorn (1973a) selected value: PrF3 Suvorov et al. (1966) Zmbov and Margrave (1968) Skinner and Searcy (1968) selected value:

414.1 453.9 454 ± 5.0 continued on next page

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

235

Table E.1, continued from previous page methoda

T /K

sub H ◦ (298.15 K)/kJ·mol−1

M M

992–1167 1325–1437

445.9 450.8 450.4 ± 5.0

E M M M M

1326–1362 1426–1622 1002–1170

452.1 ± 0.3 445.0 ± 0.5

e

455.7 ± 0.1 449.5 448.6 ± 3.0

E M M

1328–1406 1278–1456

E M M M

1311–1405 1374–1521

TmF3 Zmbov and Margrave (1967) Biefeld and Eick (1976) Bencze et al. (1996) selected value:

M K K+M

1273–1415 1349–1809 1266–1624

YbF3 Zmbov and Margrave (1967) Biefeld and Eick (1975) Petzel and Greis (1976) selected value:

M M M

1293–1428 1342–1794 1580–1795

437.9 ± 0.4 457.3 ± 2.1f 454.0 ± 0.5 454.0 ± 2.0

LuF3 Zmbov and Margrave (1967) Petzel et al. (1992) selected value:

M K

1287–1450 1471–1945

425.2 ± 0.5 440.0 ± 1.1 440.0 ± 2.0

authors TbF3 Zmbov and Margrave (1968) McCreary and Thorn (1973b) selected value: DyF3 Besenbuch et al. (1967) Zmbov and Margrave (1968) McCreary and Thorn (1974b) Stolyarova et al. (1996) selected value: HoF3 Besenbuch et al. (1967) McCreary and Thorn (1974b) selected value: ErF3 Besenbuch et al. (1967) McCreary and Thorn (1974b) Bencze et al. (1996) selected value:

1280–1380

e

e

1288–1635

448.0 ± 0.5 449.6 ± 0.3 456.8 ± 0.4 451.5 ± 2.0 454.8 ± 0.4 452.8 ± 0.2 457.3 ± 1.5 455.3 ± 0.3 454.3 ± 2.0

446.6 ± 0.4 452.6 ± 0.6 449.6 ± 3.0

a B, boiling point method; E, effusion; K, Knudsen effusion; M, mass spectrometry; TE, torsion effusion. b Also reported by Zmbov and Margrave (1968). c Made on a sample (Pr 1/3 Pm1/3 Sm1/3 )F3 . d Mean temperature. e No temperature range given. f It was concluded by the authors that the vaporization proceeded according to the reaction YbF 3.00 (cr) = 0.005YbF2.40 (cr) + 0.95YbF3 (g) + 0.003F(g). We have here treated the data as if congruent vaporization took place.

236

R.J.M. KONINGS AND A. KOVÁCS Table E.2 Enthalpy of sublimation of the gaseous lanthanide trichlorides methoda

T /K

sub H ◦ (298.15 K)/kJ·mol−1

K K B B K K M B TE

1028–1192 842–1101 ????–1673 1397–1493 1022–1110 1173–1253 950–1100 1373–1573 955–1045

331.9 ± 0.8 329.8 ± 1.3 333.2 340.2 ± 1.0 342.7 ± 0.3 319.7 ± 4.3 331.4 337.1 337.8 ± 0.2 337.5 ± 5.0

CeCl3 Harrison (1952) Novikov and Baev (1962) Shimazaki and Niwa (1962) Moriarity (1963) Polyachenok and Novikov (1963b) Villani et al. (2000b) Pogrebnoi et al. (2001) Kapala et al. (2002) selected value:

K B K K B TE M M

1013–1085 1366–1497 1012–1071 1043–1223 ????–1673 887–1003 972–1075 876–1088

326.0 ± 1.6 332.3 ± 0.8 332.8 ± 0.2 323.7 ± 1.9 312.3 329.1 ± 0.1 333.5 ± 0.3 327.1 330.3 ± 3.0

PrCl3 Harrison (1952) Novikov and Baev (1962) Shimazaki and Niwa (1962) Moriarity (1963) Polyachenok and Novikov (1963b) Dudchik et al. (1969a) Nisel’son et al. (1978) Hannay and Myers (1979) Villani et al. (2000a) Kapala et al. (2002) selected value:

K B K K B B B E TE M

991–1142 1314–1465 1002–1061 1002–1273 ????–1673 1374–1636 1373–1573 914–1056 890–1061 946–1106

320.9 ± 1.8 329.9 ± 0.7 330.6 ± 0.2 330.6 ± 0.2 323.3 ± 3.6 327.5 ± 0.2 336.4 332.1 ± 0.5 327.7 ± 0.3 326.1 329.2 ± 3.0

NdCl3 Harrison (1952) Novikov and Baev (1962) Shimazaki and Niwa (1962) Moriarity (1963) Polyachenok and Novikov (1963b) Ciach et al. (1973) Evseeva and Zenkevich (1976) Nisel’son et al. (1978) Villani et al. (2002) Kapala et al. (2002) selected value:

K B K K B M M B TE M

964–1107 1314–1465 973–1032 993–1278 ????–1673 1055–1093

authors LaCl3 Harrison (1952) Nesmeyanov and Sazonov (1959) Polyachenok and Novikov (1963b) Novikov and Baev (1962) Shimazaki and Niwa (1962) Moriarity (1963) Hastie et al. (1968) Nisel’son et al. (1978) Brunetti et al. (2000) selected value:

1373–1573 866–1019 934–1079

312.6 ± 2.2 324.0 ± 0.8 326.7 ± 0.5 323.6 ± 4.2 293.0 339.0 n.a. 329.1 324.5 ± 0.3 323.8 324.5 ± 2.0 continued on next page

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

237

Table E.2, continued from previous page methoda

T /K

sub H ◦ (298.15 K)/kJ·mol−1

? M

774–854 972–1075

247.6 299.0 ± 0.4 315 ± 8

EuCl3 Moriarity (1963) Hastie et al. (1968) selected value:

E M

953–1188 1145–1290

275.8 ± 10.6 decomp. 310.0 ± 10

GdCl3 Moriarity (1963) Dudchik et al. (1969a) Ciach et al. (1973) Myers and Hannay (1980) selected value:

K B M E

871–1119 1369–1603 963–1075 938–1044

291.4 ± 3.4 304.1 ± 0.4 320.9 307.9 ± 0.5 306.0 ± 6.0

TbCl3 Moriarity (1963) Dudchik et al. (1969a) Myers and Hannay (1980) Kudin et al. (2000) selected value:

K B K M

1198–1313 1326–1653 926–1044 900–1100

300.5 ± 6.2 295.1 ± 0.3 300.3 ± 0.4 308.6 297.7 ± 3.0

DyCl3 Moriarity (1963) Dudchik et al. (1969a) Myers and Hannay (1980) Kudin et al. (1997) Brunetti et al. (1999) Kapala et al. (2002) selected value:

K B K M TE M

1023–1223 1325–1620 936–1031 850–1010 924–1214 930–1027

269.8 ± 1.1 282.6 ± 0.5 287.9 ± 0.4 275.1 283.7 ± 0.2 282.4 284.2 ± 4.0

HoCl3 Moriarity (1963) Dudchik et al. (1969b) Piacente et al. (2002) selected value:

K B TE

1043–1223 1273–1643 904–1105

275.1 ± 3.2 279.8 284.8 ± 0.3 284.8 ± 4.0

ErCl3 Moriarity (1963) Polyachenok and Novikov (1963b) selected value:

K B

1043–1283 ????–1673

285.8 ± 9.2 264.0 285 ± 8

TmCl3 Moriarity (1963) Dudchik et al. (1969b) Kudin et al. (2000) selected value:

K B M

1073–1228 1273–1643 900–1100

authors SmCl3 Pashinkin et al. (1962) Pogrebnoi et al. (2001) selected value:

274.6 ± 5.9 276.2 283.2 276 ± 6 continued on next page

238

R.J.M. KONINGS AND A. KOVÁCS Table E.2, continued from previous page

authors YbCl3 Moriarity (1963) Kudin et al. (1997) selected value: LuCl3 Moriarity (1963) Dudchik et al. (1969b) Nisel’son et al. (1978) selected value:

methoda

T /K

sub H ◦ (298.15 K)/kJ·mol−1

K M

1148–1323 1000–1130

292.1 ± 1.4 309.4 277 ± 6

K B B

1168–1228 1273–1643 1373–1573

283.9 ± 2.1 277.1 277 ± 6

a B, boiling point method; E, effusion; K, Knudsen effusion; M, mass spectrometry; TE, torsion effusion.

Table E.3 Enthalpy of sublimation of the gaseous lanthanide tribromides methoda

T /K

sub H ◦ (298.15 K)/kJ·mol−1

K K B M TE

915–1057 1002–1052 1321–1542 950–1024 955–1045

295.0 ± 1.4 321.4 ± 0.1 318.0 308.8 ± 0.6 316.0 ± 0.1 314.3 ± 5.0

CeBr3 Harrison (1952) Shimazaki and Niwa (1962) Dudchik et al. (1975) Gietmann et al. (1996) Villani et al. (2000b) selected value:

K E B M TE

892–1030 943–992 1306–1518 962–968 887–1003

286.8 ± 0.8 311.8 ± 0.4 308.4 301.1 ± 0.0 305.9 ± 0.4 306.8 ± 5.0

PrBr3 Shimazaki and Niwa (1962) Dudchik et al. (1975) Gietmann et al. (1996) Villani et al. (2000a) selected value:

K B M TE

924–973 1280–1560 924–955 890–1061

307.4 ± 0.3 304.4 298.1 ± 0.2 303.0 ± 0.2 303.3 ± 4.0

NdBr3 Harrison (1952) Shimazaki and Niwa (1962) Dudchik et al. (1975) Gietmann et al. (1996) Villani et al. (2002) selected value:

K K B M TE

849–975 889–948 1258–1559 923–936 866–1019

274.2 ± 0.4 305.6 ± 0.1 302.2 294.6 ± 0.2 304.2 ± 0.2 301.6 ± 4.0

SmBr3 Harrison (1952) selected value:

K

822–940

authors LaBr3 Harrison (1952) Shimazaki and Niwa (1962) Dudchik et al. (1975) Gietmann et al. (1996) Brunetti et al. (2000) selected value:

260.2 ± 1.4 300 ± 10 continued on next page

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

239

Table E.3, continued from previous page methoda

T /K

sub H ◦ (298.15 K)/kJ·mol−1

B M

1120–1532 1005–1011

277.0 272.5 ± 0.1 274.8 ± 3.0

TbBr3 Makhmadmurodov et al. (1975) Gietmann et al. (1996) selected value:

B M

1219–1536 964–985

274.6 270.6 ± 0.5 272.6 ± 3.0

DyBr3 Makhmadmurodov et al. (1975) Hilpert et al. (1995) Brunetti et al. (1999) selected value:

B M TE

1220–1535 953–1053 878–1151

273.0 269.6 ± 0.4 276.4 ± 0.4 273.0 ± 5.0

HoBr3 Gietmann et al. (1996) Piacente et al. (2002) selected value:

M TE

971–1003 904–1105

275.0 ± 0.5 285.0 ± 0.3 280.0 ± 5.0

ErBr3 Makhmadmurodov et al. (1975) Gietmann et al. (1996) selected value:

B M

1242–1506 946–995

270.8 271.4 ± 0.8 271.1 ± 5.0

TmBr3 Makhmadmurodov et al. (1975) Gietmann et al. (1996) selected value:

B M

1252–1482 946–995

269.5 275.4 ± 1.7 272.5 ± 5.0

LuBr3 Makhmadmurodov et al. (1975) selected value:

B

1305–1468

267.2 267.2 ± 10

authors GdBr3 Makhmadmurodov et al. (1975) Gietmann et al. (1996) selected value:

a B, boiling point method; E, effusion; K, Knudsen effusion; M, mass spectrometry; TE, torsion effusion.

Table E.4 Enthalpy of sublimation of the gaseous lanthanide triiodides authors LaI3 Shimazaki and Niwa (1962) Hirayama et al. (1976) Brunetti et al. (2000) selected value: CeI3 Hirayama and Castle (1973) Hirayama et al. (1975) Struck and Feuersanger (1999) Villani et al. (2000b) selected value:

methoda

T /K

sub H ◦ (298.15 K)/kJ·mol−1

K M TE

953–1012 891–1009 955–1045

315.5 ± 0.4 302.7 ± 0.3 307.9 ± 0.3 307.9 ± 8.0

M K M TE

933b 870–1015 841–928 887–1003

305.9 297.5 ± 0.4 285.6 301.8 ± 0.4 299.7 ± 5.0 continued on next page

240

R.J.M. KONINGS AND A. KOVÁCS Table E.4, continued from previous page methoda

T /K

sub H ◦ (298.15 K)/kJ·mol−1

E E TE

933–1002 841–1032 890–1061

303.6 ± 0.7 296.5 ± 0.7 297.1 ± 0.3 296.8 ± 3.0

NdI3 Shimazaki and Niwa (1962) Hirayama and Camp (1972) Villani et al. (2002) selected value:

E E TE

953–1002 857–1037 866–1019

298.0 ± 0.3 289.7 ± 0.6 296.0 ± 0.2 294.6 ± 3.0

GdI3 Hirayama and Castle (1973) Hirayama et al. (1975) selected value:

M K

943b 912–1025

270.0 276.4 ± 0.8 276.4 ± 4.0

TbI3 Hirayama and Castle (1973) Hirayama et al. (1975) selected value:

M K

931b 883–979

261.0 273.0 ± 0.4 273.0 ± 6.0

DyI3 Hirayama and Castle (1973) Hirayama et al. (1975) Kaposi et al. (1983) Brunetti et al. (1999) selected value:

M K M TE

916b 885–1060 970–1150 843–1051

266.7 272.6 ± 0.4 270.8 ± 1.7 274.9 ± 0.4 273.8 ± 4.0

HoI3 Hirayama and Castle (1973) Hirayama et al. (1975) Kaposi et al. (1986) Gietmann et al. (1996) Piacente et al. (2002) selected value:

M E M M TE

880b 924–1029 935–1055 945–975 904–1105

280.7 276.1 ± 0.6 275.3 ± 0.5 269.3 ± 0.8 267.1 ± 0.4 272.0 ± 6.0

ErI3 Hirayama and Castle (1973) Hirayama et al. (1975) selected value:

M K

895b 898–1016

259.9 273.5 ± 0.6 273.5 ± 6.0

TmI3 Hirayama et al. (1975) Dettingmeijer and Dielis (1988) Struck and Feuersanger (1991) selected value:

K K M

867–990 874–1012 775–900

271.8 ± 0.6 267.5 ± 0.4c 258.1 271.8 ± 6.0

authors PrI3 Shimazaki and Niwa (1962) Hirayama and Camp (1972) Villani et al. (2000a) selected value:

a B, boiling point method; E, effusion; K, Knudsen effusion; M, mass spectrometry; TE, torsion effusion. b Only mean temperature is given. c Recalculated assuming momomeric species only.

THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES

241

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Handbook on the Physics and Chemistry of Rare Earths Vol. 33 edited by K.A. Gschneidner, Jr., J.-C.G. Bünzli and V.K. Pecharsky © 2003 Elsevier Science B.V. All rights reserved

Chapter 214 RARE EARTH –MANGANESE PEROVSKITES John B. GOODENOUGH University of Texas at Austin, Austin, TX 78712-1063, USA

Contents

List of acronyms 1. Introductory concepts 1.1. Tolerance factor 1.2. Electronic considerations 1.2.1. Ligand-ﬁeld considerations 1.2.2. Interatomic interactions 1.2.3. Localized-itinerant electronic transitions 2. Single-valent perovskites 2.1. LaMnO3 2.2. LaMn1−x Gax O3 and LaMn1−x Scx O3 2.3. RMnO3 2.4. CaMnO3 2.5. SrMnO3

249 250 250 252 253 256 260 262 262 269 275 276 277

2.6. Sr1−x Cax MnO3 (0 x 1) and Sr1−y Bay MnO3 (0 y 0.2) 2.7. Bloch’s rule 3. Mixed-valent perovskites 3.1. Oxygen vacancies 3.2. Ca1−x Lax MnO3 , 0 x 0.2 3.3. LaMnO3+δ 3.4. (La1−y Ry )0.7 A0.3 MnO3 : The CMR phenomenon 3.5. The system La1−x Srx MnO3 3.6. The system La1−x Cax MnO3 3.7. R0.5 A0.5 MnO3 4. Conclusions References

List of acronyms AFI AFM

antiferromagnetic insulator antiferromagnetic metal

MCG NMR

magnetic cluster glass nuclear magnetic resonance

CO CAFI

charge-ordered canted-spin antiferromagnetic insulator

NQR OO

nuclear quadrupole resonance orbital-ordered

CDW

charge-density wave

PDF

pair-density function

CMR ESR

colossal negative magnetoresistance electron spin resonance

QCP SG

quantum critical point spin glass

FC

ﬁeld-cooled

SDW

spin-density wave

FI FM

ferromagnetic insulator ferromagnetic metal

SP ZFC

superparamagnetic zero-ﬁeld-cooled

FV

ferromagnetic vibronic conductor

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278 279 282 282 283 285 290 311 323 330 342 344

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1. Introductory concepts 1.1. Tolerance factor The cubic AMO3 perovskite structure consists of an MO3 array of corner-shared MO6/2 octahedra with a large A cation at the body-center position. As is illustrated in ﬁg. 1, this structure allows formation of the Ruddlesden–Popper (1957, 1958) rock-salt/perovskite intergrowth structures MO · (AMO3 )n . In all these structures, the mismatch between the equilibrium (A–O) and (M–O) bond lengths is given by the deviation from unity of the geometric tolerance factor √ t ≡ (A–O)/ 2(M–O). (1) This factor may be calculated for room temperature and atmospheric pressure from tabulated sums of ionic radii obtained from X-ray data (Shannon and Prewitt, 1969, 1970). However, it must be recognized that the thermal expansions and the compressibilities of the (A–O) and (M–O) bonds are different, which makes t both pressure and temperature dependent. In the case of a transition-metal atom M, the thermal expansion of the (A–O) bond is the larger, which makes dt/dT > 0.

(2)

The compressibility of the (A–O) bond is normally the larger (Goodenough et al., 1972), which makes dt/dP < 0,

(3a)

but at the crossover from localized to itinerant electronic behavior for d electrons of an MO3 array, a dt/dP > 0

(3b)

is found. The origin of this abnormality is discussed in sect. 1.2.3.

(a)

(b)

Fig. 1. (a) The ideal cubic perovskite structure and (b) the n = 1 Ruddlesden–Popper phase AO · AMO3 .

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Fig. 2. The hexagonal perovskite polytypes: (a) cubic, (b) hexagonal, (c) 6H, (d) 4H, (e) 9R after Goodenough et al. (1972).

The AMO3 perovskites adjust to a t > 1 by the formation of hexagonal polytypes like those illustrated schematically in ﬁg. 2. In these polytypes, the close-packed (111) AO3 layers of the cubic phase are changed from all-cubic to cubic + hexagonal or all-hexagonal stacking. Application of hydrostatic pressure normally reduces t, changing hexagonal polytypes successively to structures with more cubic and less hexagonal stacking (Goodenough et al., 1972). The AMO3 perovskites adjust to a t < 1 by cooperative rotations of the MO6/2 octahedra. These rotations lower the M–O–M bond angle from 180◦ to (180◦ − φ). Three of the common rotations are illustrated in ﬁg. 3. With decreasing t, rotations about a cubic [001] axis to give tetragonal I4/mcm symmetry is followed by those about a [111] axis to give rhombohe¯ symmetry and then about a [110] axis to give orthorhombic Pbnm symmetry with dral R 3c √ √ c/a > 2 (in the equivalent space group Pnma, b/a > 2). The bending angle φ increases ¯ to Pbnm symmetry. with decreasing t, and φ increases discontinuously on going from R 3c The Ruddlesden–Popper phases also adjust to a t < 1 by cooperative rotations of the MO6/2 octahedra. The ability to adjust to a t < 1 allows for extensive cation substitutions on both the A and the M sites; the structure is also tolerant of large concentrations of both oxygen and A-cation vacancies. The perovskites do not accept oxygen interstitials, but the Ruddlesden–Popper phases with a t < 1 may accept interstitial oxygen between the AO layers of the rock-salt intergrowths in order to increase t. Primary emphasis here is on the oxygen-stoichiometric perovskites containing M = Mn; the physical properties of these oxides are changed either by a progressive substitution of a lanthanide by an alkaline-earth on the A sites so as to change both t and the Mn(IV)/Mn ratio or by a progressive isovalent substitution of one rare-earth by another or one alkaline-earth by another on the A sites so as to change only t while keeping the Mn(IV)/Mn ratio ﬁxed. The of two or more A-site cations of different radius presence 2 − r 2 ), where x is the concentration of each A-site rA leads to a variance σ 2 ≡ ( i xi rAi A i cation of radius rAi ; σ 2 is a measure of the consequent perturbation of the periodic potential of the MO3 array. Partial substitutions of Mn by other cations on the M sites are also discussed for a few special cases. Several interesting phenomena encountered in Ruddlesden–Popper manganites are not included here.

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(a)

(c)

(b)

Fig. 3. Common MO6/2 cooperative rotations about (a) [001] to give tetrag¯ (c) [110] to onal I4/mcm symmetry, (b) [111] to give rhombohedral R 3c, give O-orthorhombic Pbnm (or Pnma).

1.2. Electronic considerations The AMO3 perovskites with M = Mn are sufﬁciently ionic that the Madelung energy stabilizes ﬁlled bonding bands that have primarily O-2p character separated from empty antibonding bands of primarily cationic s and p character by a large (∼ 6 eV) energy gap. Lanthanide A-site cations introduce empty 5d bands that may overlap the antibonding s bands (Oliver et al., 1972). The 4fn conﬁgurations at the A-site lanthanide ions are localized and the intraatomic electron–electron coulomb energies are large, so the separation between successive 4fn conﬁgurations is Ufn > 6 eV. Moreover, the Ce4+ ion is too small to occupy an A site, the Eu3+ /Eu2+ redox energy lies above the Mn(III)/Mn(II) level, and the Pr4+ /Pr3+ redox energy lies below the Mn(IV)/Mn(III) level. As illustrated schematically in ﬁg. 4 for NdMnO3 , the Mn(IV)/Mn(III) redox energy lies a little above the top of the O-2p bonding bands. Therefore, in the manganese perovskites to be discussed, the rare-earth ions all have R3+ : 4f0 or localized R3+ : 4fn conﬁgurations with 4f-electron energies well-removed from the Fermi energy. Long-range magnetic ordering of the R3+ : 4fn conﬁgurations at low-temperatures is not considered here; the principal interest of the R3+ ion is its size, which inﬂuences the physical properties of the MnO3 array through the tolerance factor t and variance σ 2 .

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Fig. 4. Schematic one-electron energies for Nd-5d, 6s and O-2p bands of NdMnO3 and redox energies of Nd(III) and Mn(III) in NdMnO3 .

The structural, transport, and magnetic properties of a manganese-perovskite system R1−x Ax MnO3 (A = alkaline-earth or alkali atom) are strongly inﬂuenced by two features of the MnO3 array: the orbital degeneracy of the octahedral-site, high-spin Mn(III) : d4 conﬁguration and the possibility of a transition from localized to itinerant electronic behavior of the σ -bonding d electrons with increasing t and Mn(IV)/Mn ratio x. Therefore, we introduce a description of the d-electron manifold before we present and interpret the physical data. 1.2.1. Ligand-ﬁeld considerations The ﬁve 3d orbitals of a free Mn atom are degenerate; but with more than one electron in the 3d manifold, the spin degeneracy is removed by the ferromagnetic direct-exchange interactions between electron spins in atomic orthogonal orbitals. These exchange interactions produce the Hund intraatomic exchange ﬁeld Hex . The exchange splitting between spin states will be designated Δex . |m| The atomic orbitals fm = Rnl (r)Pl (cos θ ) exp(±imφ) with azimuthal angular momentum quantum number m, where Lz fm = −i h¯ (∂fm /∂φ) = mh¯ fm , have the angular dependencies for l = 2 (d orbitals)

f0 ∼ cos2 θ − 1 ∼ z2 − x 2 + z2 − y 2 /r 2 , f±1 ∼ sin 2θ exp(±iφ) ∼ (yz ± izx)/r 2,

f±2 ∼ sin2 θ exp(±i2φ) ∼ x 2 − y 2 ± ixy /r 2 .

(4)

In an isolated octahedral site, the xy and (yz ± izx) orbitals only overlap the ligand O-2pπ orbitals while the [(z2 − x 2 ) + (z2 − y 2 )] and (x 2 − y 2 ) orbitals only overlap the O-2s, 2pσ orbitals. The resonance integrals bca ≡ (fm , H φo ) ≈ εmo (fm , φo ) describing the energy of a virtual charge transfer to the empty M-3d orbitals from the same-symmetry sum of nearneighbor oxygen orbitals φo contain both an overlap integral (fm , φo ) and a one-electron energy εmo that are larger for σ -bonding than for π -bonding. Therefore, the antibonding states

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(a)

(b)

Fig. 5. Octahedral-site splitting of (a) the orbitally ﬁvefold-degenerate d1 manifold by a cubic crystalline ﬁeld and (b) the high-spin Mn(III) conﬁguration.

of a σ -bond are raised higher in energy than those of a π -bond and, as a consequence, the cubic symmetry of the octahedral site raises the twofold-degenerate pair of σ -bonding e orbitals, the [(z2 − x 2 ) + (z2 − y 2 )] and the (x 2 − y 2 ) orbitals, above the threefold-degenerate set of π -bonding t orbitals xy, (yz ± izx) by an energy Δc , which quenches the orbital angular momentum associated with m = ±2 (see ﬁg. 5). If a point-charge ionic model places the empty 3d orbitals of a degenerate manifold an energy ΔEp above the O-2p orbitals and ΔEs above the O-2s orbitals, the antibonding d-like states may be described in second-order perturbation theory to give the ligand-ﬁeld wavefunctions ψt = Nπ (ft − λπ φπ ), ψe = Nσ (fe − λσ φσ − λs φs ),

(5)

provided the covalent-mixing parameters are λπ ≡ 1 and λσ ≡ 1. A larger ΔEs keeps λs 1 where eq. (5) is applicable. According to second-order perturbation theory, the antibonding states are raised an energy ΔE = |bca |2 /ΔEp by the Mn–O covalent bonding, and the cubic-ﬁeld splitting of the e and t orbital energies is

Δc = Δεσ − Δεπ = ΔM + λ2σ − λ2π ΔEp + λ2s ΔEs , (6) bπca/ΔEp

bσca/ΔEp

where ΔM is a small, purely electrostatic energy of uncertain sign due to the penetration of the O2− -ion electron cloud by the cation wavefunctions. In the perovskite structure, an interaction of the ψt electrons with the empty A-cation wavefunctions would lower επ and increase Δc . This latter interaction does not appear to be of primary importance in the rare-earth manganese perovskites where a Δex > Δc removes the spin degeneracy and maintains, at atmospheric pressure, a high-spin conﬁguration on the Mn(III) : t3 e1 ions; the Mn(IV) : t3 e0 conﬁguration contains no e electron and the high-spin Mn(II) : t3 e2 conﬁguration has two electrons in a σ -bonding e-orbital. The mobile electrons that transport charge are electrons occupying the orbitally twofold-degenerate e orbitals.

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(a)

(b)

(i)

(ii)

Fig. 6. (a) Jahn–Teller octahedral-site deformations that remove the e-orbital degeneracy of a localized Mn(III) : t3 e1 conﬁguration. (b) Cooperative oxygen displacements that remove the orbital degeneracy of a high-spin, octahedralsite d4 conﬁguration: (i) disproportionation as in CaFeO3 below room temperature and (ii) Jahn–Teller orbital ordering in LaMnO3 .

The twofold e-orbital degeneracy at a localized Mn(III) : t3 e1 conﬁguration may be removed by cooperative oxygen displacements that either lower the site symmetry from cubic to tetragonal or orthorhombic (Jahn–Teller site distortion) as illustrated in ﬁg. 6(a) or transfer an electron from one Mn atom to another as in the disproportionation reaction 2Mn(III) = Mn(IV) + Mn(II) that is illustrated in ﬁg. 6(b)(i). These atomic displacements are superimposed on the cooperative rotations of the MnO6/2 octahedra induced by a tolerance factor t < 1. In a perovskite with a large concentration of Mn(III) ions, long-rangecooperative Jahn–Teller site distortions reduce the elastic energy associated with the individual site distortions and give a global distortion of the structure. In orthorhombic LaMnO3 , for example, long-range orbital ordering stabilizes site distortions that create within (001) planes two short and two long Mn–O bonds at each site-centered Mn atom, the direction of the long Mn–O bonds alternating from (100) to (010) in a checkerboard fashion as is illustrated in ﬁg.√6(b)(ii). The√ long-range orbital ordering changes the orthorhombic axial ratio from c/a > 2 to c/a < 2. Where the local site distortions are disordered, the axial √ √ ratio becomes c/a ≈ 2. We distinguish the orthorhombic structures as O for a c/a > 2 due

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√ to cooperative MnO6/2 rotations alone, O for a c/a < 2 signaling a superimposed long√ ∗ range-cooperative orbital ordering, and O for c/a ≈ 2 signaling orbital ﬂuctuations with only short-range-cooperative orbital ordering. 1.2.2. Interatomic interactions In the manganese perovskites, the dominant interactions between d-like orbitals at neighboring Mn atoms are the (180◦ − φ) Mn–O–Mn interactions. The spin-independent resonance integrals describing charge transfer between Mn atoms at positions Ri and Rj are

bπcac = ψt i , H ψtj ≈ επ λ2π ,

bσcac = ψei , H ψej ≈ εσ λ2σ cos φ, (7) where λπ varies with the acidity of the A cations as well as with the bending angle φ and H describes the perturbation of the potential at Rj caused by the presence of a Mn atom at Ri . The smaller term εs λ2s is omitted from bσcac for simplicity. The interactions between localized spins on neighboring cations are treated by a perturbation theory in which the spin-dependent resonance integrals for parallel and antiparallel coupling of spins are ↑↑

↑↓

tij = bijcac cos(θij /2) and tij = bijcac sin(θij /2)

(8)

for electron transfer between cations whose spins are rotated by an angle θij with respect to one another; bijcac ≈ εij (ψi , ψj ) is the spin-independent resonance integral. The spin angular momentum is conserved in an electron transfer. Rules for the sign of the interatomic spin–spin exchange interactions follow: • Direct exchange between spins in orthogonal orbitals is a potential exchange as it does not involve electron transfer; like the intraatomic interactions, it is ferromagnetic. • Superexchange interactions between spins Si and Sj on neighboring atoms is a kinetic exchange that involves virtual charge transfer between crystal-ﬁeld orbitals on neighboring cations; spin polarization of the electron cloud on any intervening anion is neglected in this Anderson (1959) formulation of superexchange. However, Goodenough (1963) pointed out that where the superexchange interaction is across an intervening anion, as in the (180 − φ) Mn–O–Mn interactions in a manganese-oxide perovskite, there is an additional component to the superexchange interaction, which he called “semicovalent exchange” as it involves transfer of two electrons from the intervening oxygen, one each to the two interacting transition-metal atoms. This term does not change the sign of the overall exchange interaction; but it adds a second semicovalent-exchange term to the expression for the superexchange interaction that becomes dominant where the energy ΔEp becomes smaller than the effective intraatomic energy Ueff (Zaanen and Sawatzky, 1987). We shall introduce this second term explicitly in the discussion of the single-valent compounds LaMnO3 and CaMnO3 (sects. 2.4 and 2.7). Here we present only the Anderson formulation and its modiﬁcation to give the rules for the sign of the superexchange spin–spin coupling. Antiferromagnetic superexchange: Transfer of an electron of α spin from a half-ﬁlled orbital to an orbital that is also half-ﬁlled is constrained by the Pauli exclusion principle to be most

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probable if the spin on the acceptor atom has β spin. From second-order perturbation theory, the bonding energy gained by the virtual electron transfer is, from eq. (8), ↑↓ 2 ΔεS ≈ −tij /Ueff = Const + Jij Si · Sj (9) where Jij ≈ |2bij2 |/4S 2 Ueff and Ueff is the total energy it costs to add an electron to the acceptor. Equation (9) with Jij ≈ 2bij2 /Ueff is the Anderson expression for spin S = 1/2. Ferromagnetic superexchange: Transfer of an electron from a half-ﬁlled orbital to an empty orbital on an acceptor atom having a spin S is not constrained by the Pauli exclusion principle, but the intraatomic exchange energy Δex makes the transfer most probable if the spin S is parallel to the spin of the transferred electron. From third-order perturbation theory, the bonding energy gained by the virtual electron transfer is, from eq. (8), ↑↑

Δε ≈ − S

|tij |2 Δex 2 Ueff

= Const − Jij Si · Sj

(10)

2 . where Jij ≈ (2bij2 Δex )/4S 2 Ueff A similar reasoning applies to virtual transfer of an electron from a ﬁlled orbital at an atom of spin S to a half-ﬁlled orbital at an acceptor atom. Vibronic superexchange: In manganese-oxide perovskites, orbital ﬂuctuations at the Jahn– Teller Mn(III) ions of a Mn(III)–O–Mn(III) interaction give rise, over the period of an axial oxygen vibration, to both antiferromagnetic and ferromagnetic superexchange interactions. However, electron transfer to an empty orbital is energetically favored over transfer to a halfﬁlled orbital and the axial oxygen displacements associated with the orbital ﬂuctuations correlate asymmetric e-orbital occupancy on either side of the oxygen atom for minimization of the elastic energy. Consequently, the net vibronic Mn(III)–O–Mn(III) superexchange interaction is ferromagnetic. • Double exchange is also a kinetic exchange; it involves a real charge transfer between like atoms in two different valence states, each carrying a localized spin S. If the charge transfer requires an activation energy as occurs in polaronic conduction, then the individual atomic spins have time to relax between electron jumps and no spin–spin coupling is achieved by the real charge transfer. In this case, a superexchange coupling by virtual charge transfer is still present. Polaronic conduction in a manganese-oxide perovskite occurs where the time τh for an electron to hop from one atom to a neighbor is long compared to the period ωo−1 of the cooperative oxygen vibrations that would trap it at the manganese atom of lower valence state. Double exchange was ﬁrst postulated by Zener (1951) to occur within a Mn(III)– O–Mn(IV) pair by a double electron transfer O2− –Mn(IV) = O− –Mn(III) accompanied by Mn(III)–O− = Mn(IV)–O2− on the opposite side in a time τh < ωo−1 to give a ferromagnetic coupling between localized manganese spins since spin is conserved in the real charge transfer and the intraatomic Δex is operative at each Mn atom. This mechanism only provides for ferromagnetically coupled pairs

Mn(III)–O–Mn(IV) = Mn(IV)–O–Mn(III),

(11)

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In order to account for an observed global ferromagnetism, Zener (1951) had to make the further assumption that these pairs do not require an activation energy to diffuse through the lattice. This model leads to a charge-carrier mobility μ = eDo /kT

(12)

where the diffusion coefﬁcient Do is temperature-independent. We shall refer to the twomanganese polarons described by eq. (11) as Zener polarons. Following the formulation of eq. (8) by Anderson and Hasegawa (1955). De Gennes (1960) proposed a double-exchange model in which the mobile electrons of e-orbital parentage occupy a narrow σ ∗ band hav↑↑ ing no spin degeneracy and a spin-dependent resonance integral tij replaces the usual spinindependent integral bijcac . The tight-binding band model then gives a ferromagnetic stabilization ↑↑

cac ΔD ex ≈ −c(1 − c)ztij = −c(1 − c)zbij cos(θij /2)

(13)

where z is the number of manganese near neighbors and c = Mn(IV)/Mn is the fractional occupancy of mobile charge carriers in the MnO3 array. • Indirect exchange is a coupling of localized spins at M atoms by electrons of a partially occupied broad band. Whereas the mobile spins are assumed to couple ferromagnetically to the localized spins in the De Gennes model (minority-spin electrons would couple antiferromagnetically), localized spins only induce a partial intraatomic parallel-spin magnetization of broad-band electrons. The induced magnetization is largest at the position of a localized spin and it oscillates in sign at larger distances from the localized spin. Therefore, indirect exchange may be ferromagnetic between close near neighbors and antiferromagnetic between more distant neighbors. • Antisymmetric exchange introduces a term of the form D ij · S i × S j that may be added to the symmetric superexchange term of the form Jij S i · S j ; it cants antiferromagnetically coupled spins so as to give a ferromagnetic component perpendicular to the vector D ij . Antisymmetric exchange originates in the orbital angular momentum; it may dominate symmetric exchange in the coupling between localized 4fn conﬁgurations on the lanthanide ions, but it is much weaker than the symmetric exchange in the coupling between dn conﬁgurations in the manganese-oxide perovskites. Antisymmetric exchange was introduced by Dzialoshinskii (1958), who pointed out that a D ij = 0 can only exist where spin canting leaves the system invariant under all symmetry operations of the unit cell. The formalism was developed further by Moriya (1960); D ij is known as the Dzialoshinskii vector. In the orthorhombic AMO3 perovskites, canting of antiferromagnetically coupled M-atom spins to give a weak ferromagnetic component can be accomplished by any of three different mechanisms: magnetocrystalline anisotropy of cooperatively tilted MO6/2 octahedra, Dzialoshinskii–Moriya antisymmetric exchange, or a double-exchange component varying as cos(θij /2) superimposed on a superexchange component varying as cos θij . Bertaut (1963) has described the possible spin conﬁgurations compatible with the Pbnm space group. Figure 7 represents the M atoms of an orthorhombic AMO3 structure. Linear combinations of the spin components that transform into themselves are chosen as the base vectors of the

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Fig. 7. Labeling of M-atom positions in the orthorhombic (Pbnm) structure of an AMO3 perovskite.

irreducible representations. In the notation of Koehler et al. (1960), these base vectors are F = S1 + S2 + S3 + S4, G = S1 − S2 + S3 − S4,

(14)

C = S1 + S2 − S3 − S4, A = S1 − S2 − S3 + S4.

Subjecting these vectors to the crystallographic symmetry operations generates the four possible representations of the base vectors shown in table 1. The x, y, z directions in table 1 are taken parallel to the a, b, c axes of the orthorhombic unit cell in space group Pbnm. Where the MO3 array is mixed-valent with both orbital and charge ordering, more complex spin conﬁgurations are found as is illustrated by La0.5 Ca0.5 MnO3 . Extrapolation of the rules for the sign of the superexchange interaction, eqs. (9) and (10), to itinerant-electron magnetism leads to the following rules for bands containing n electrons per band orbital (0 n 2 because of spin degeneracy): • Half-ﬁlled bands (n = 1) are antiferromagnetic. • Bands with 0 < n 1/2 or 3/2 n < 2 would be half-metallic ferromagnets with full magnetization M = NnμB or N(2 − n)μB per band orbital, where N is the number of transition-metal atoms per unit volume if narrow enough for total removal of the spin deTable 1 Representations of base vectors of M-atom spins with space group Pbnm Representations 1 2 3 4

Base Ax Fx Cx Gx

Vector for Gy Cy Fy Ay

M-atom spin Cz Gz Az Fz

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generacy; if the intraatomic electron–electron interactions are not strong enough to remove completely the spin degeneracy of the band, a spin-density wave (SDW) may be stabilized. • Bands with 1/2 < n < nc or nc < n < 3/2 would be ferromagnetic with a reduced magnetization M = N(1 − n)μB or M = N(n − 1)μB since only the antibonding states of the band are magnetized. At nc ≈ 2/3 or 4/3 (value depends on bandwidth), there is a transition to antiferromagnetic order as the ﬁlling approaches n = 1. The transition from localized to itinerant electronic behavior occurs where the interatomic interactions become greater than the intraatomic interactions. A measure of the strength of the interatomic interactions is the bandwidth W and of the strength of the intraatomic interactions is the energy Ueff that separates successive redox energies. The transition from localized to itinerant electronic behavior occurs where W ≈ Ueff .

(15)

Itinerant-electron magnetism is found in a narrow range of bandwidths ΔW near W ≈ Ueff . For broader bands, localized spins on the M atoms are suppressed, and the tight-binding bandwidths are Wπ ≈ 2zbπcac

and Wσ ≈ 2zbσcac

(16)

where the number of like nearest neighbors is z = 6 for 3D bands, z = 4 for 2D bands, z = 2 for 1D bands. From eq. (7), a λσ > λπ and a small bending angle φ makes Wσ > Wπ .

(17)

The intraatomic interactions, on the other hand, are stronger the weaker the covalent mixing, which makes the on-site coulomb energies Uπeff > Uσeff .

(18)

Equation (18) is particularly strong at a Mn(III) ion, for example, where Uπeff includes the exchange energy Δex whereas Uσ includes neither a crystal-ﬁeld splitting Δc nor an exchange splitting Δex . A Wπ < Uπeff can leave a t3 manifold localized in the presence of a Wσ > Uσeff that transforms the e electrons of an MO3 array into itinerant electrons occupying a narrow σ ∗ band. This situation is found, for example, in the mixed-valent MnO3 array of La1−x Srx MnO3 with 0.17 x < 0.5. 1.2.3. Localized-itinerant electronic transitions A fundamental question is whether the transition between localized and itinerant electronic behavior is continuous or discontinuous. Mott (1949) was the ﬁrst to point out that an on-site electrostatic energy Uσ > Wσ is needed to account for the fact that NiO is an antiferromagnetic insulator rather than a metal. Hubbard (1963) subsequently introduced U formally as a parameter into the Hamiltonian for band electrons; his model predicted a smooth transition from a Pauli paramagnetic metal to an antiferromagnetic insulator as the ratio W/U decreased to below a critical value of order unity. This metal–insulator transition is known as the Mott– Hubbard transition.

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In fact, there is increasing evidence that this transition is not continuous, and independent arguments have been presented that suggest the transition is ﬁrst-order (Goodenough, 1992; Dagotto et al., 1998; Rozenberg et al., 1994). The simplest argument is based on the virial theorem of mechanics for central-force ﬁelds: 2T + V = 0

(19)

where T is the mean kinetic energy of a system of particles and V is their mean potential energy. Electrons bound in a crystal have a V < 0. At a transition from localized to itinerant electronic behavior, the volume occupied by an electron increases discontinuously, which means that T decreases and therefore |V | decreases discontinuously. For antibonding electrons, a decrease in |V | is accomplished by a decrease in the equilibrium (M–O) bond length, and a discontinuous decrease in (M–O) gives a ﬁrst-order transition with (M–O)localized > (M–O)itinerant.

(20)

This situation leads to a double-well potential for the (M–O) bond at the crossover between localized and itinerant electronic behavior. A double-well potential for the equilibrium (M–O) bond length gives rise to lattice instabilities and phase segregation. However, the phase segregation may appear at too low a temperature for atomic diffusion. In this case, the perovskite structure accommodates a spinodal phase segregation by cooperative oxygen-atom displacements that create, on a small length scale, ﬂuctuating regions of shorter (M–O) bond length in a matrix of larger (M–O) bond length or vice versa with complex bond-length ﬂuctuations in between that may order at lower temperatures into a charge-density/spin-density wave (CDW/SDW); the CDW/SDW may be mobile or, if commensurate with the lattice, become pinned. A static CDW/SDW is readily observed by a diffraction experiment, a mobile CDW/SDW is not. Similarly, long-range-cooperative orbital ordering at Jahn–Teller ions induce a global lattice distortion and different equilibrium bond lengths are observed directly by neutron diffraction whereas bond-length ﬂuctuations associated with short-range-cooperative orbital ﬂuctuations are not. In the manganese oxides with perovskite structure, bond-length ﬂuctuations due to the localized-itinerant electronic crossover coexist with bond-length ﬂuctuations associated with Jahn–Teller orbital ﬂuctuations. The ﬂuctuations appearing at crossover may be called quantum-critical-point ﬂuctuations. Egami (2001) has developed pair-density-function analysis of pulsed neutron-diffraction data to determine the structure in a time interval that is short relative to a bond-length ﬂuctuation. This method provides a direct observation of the pattern of bond-length ﬂuctuations. Several other measurements have been shown to provide indirect signatures of the presence of bond-length ﬂuctuations (Goodenough and Zhou, 2001). For example, • An increase in the tolerance factor with pressure (dt/dP > 0) signals an unusually compressible M–O bond length; it has only been found at a crossover where there is a doublewell potential for two equilibrium (M–O) bond lengths. • The bandwidth W depends more sensitively on the M–O–M bond-bending angle φ than can be accounted for by eqs. (7) and (16), which suggests W = Wb exp(−λεsc /h¯ ωo ) with λ ∼ εsc /Wb ,

(21)

262

• • • • •

J.B. GOODENOUGH

where εsc is the energy required for an electron to transfer to a strong-correlation ﬂuctuation from an itinerant-electron matrix and Wb is the tight-binding bandwidth of eq. (16). The period ωo−1 of a bond-length ﬂuctuation does not need to be overly sensitive to the angle φ to make W sensitive to φ. 18 O/16 O isotope exchange changes ω−1 and thereby changes W of eq. (21) to give marked o changes in transition temperatures. The phonon contribution to the thermal conductivity is strongly suppressed by bond-length ﬂuctuations. Both the room-temperature thermoelectric power and the phonon-drag component at low temperatures increase with hydrostatic pressure due to a decrease in the volume fraction of strong-correlation ﬂuctuations in an itinerant-electron matrix. Where strong-correlation ﬂuctuations are present in an itinerant-electron matrix, the magnetic susceptibility may be interpreted as a coexistence of Curie–Weiss and mass-enhanced Pauli paramagnetism. In mixed-valent systems, a spinodal phase segregation into ﬂuctuating hole-rich conductive regions and hole-poor insulating regions gives rise to such unusual phenomena as a colossal magnetoresistance (CMR) in the manganese-oxide perovskites and high-Tc superconductivity in the intergrowth copper oxides.

2. Single-valent perovskites 2.1. LaMnO3 The most extensively studied RMnO3 parent compound is LaMnO3 , which contains highspin Mn(III) : t3 e1 ions. It was already recognized in the 1950s that this compound is oxidized in air; oxidation changes the orthorhombic, antiferromagnetic insulator LaMnO3 into a rhombohedral, ferromagnetic metal La1−ζ Mn1−ε O3 (ζ + ε = 0.12 and ζ > ε). Stoichiometric LaMnO3 is stable in an inert atmosphere like N2 or Ar or in vacuum. Wollan and at 4 K obtained by Koehler (1955) reported the structure and magnetic order of LaMnO3 √ neutron diffraction; the data showed an orthorhombic axial ratio c/a < 2 and anisotropic (180◦ − φ) Mn–O–Mn interactions with ferromagnetic (001) MnO2 planes coupled antiparallel to one another. Goodenough (1955) recognized that √ both the magnetic order below a Néel temperature TN = 135 K and an axial ratio c/a < 2 can be accounted for by a cooperative antiferrodistortive Jahn–Teller ordering of the occupied σ -bonding e orbitals to give the structure of ﬁg. 6(b)(ii). Each oxygen in a puckered (001) plane would be displaced so as to give (180◦ − φ) Mn–O· · ·Mn bonds containing one short (s) and one long (l) Mn–O bond. This order would give e1 · · ·O–e0 ferromagnetic superexchange interactions by eq. (10) that dominate the t3 –O–t3 interactions. Along the c-axis there would be no oxygen-atom displacement and equal Mn–O bonds would give antiferromagnetic t3 –O–t3 superexchange interactions by eq. (9). Although the cooperative oxygen displacements were not observed at that time, this fact could be accounted for by the limited resolving power of their early powder diffractometer. Goodenough and Loeb (1955) had previously pointed out that cooperative

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ferrodistortive Jahn–Teller orbital ordering occurs in tetragonal spinels containing octahedralsite Mn(III) and Cu(II) ions, and antiferrodistortive cooperative distortions within the (001) planes of LaMnO3 would provide an experimental demonstration of Goodenough’s postulated rules for the sign of the spin–spin superexchange interactions, rules that were later shown to have general applicability (Goodenough, 1963). Kanamori (1959, 1960) subsequently reﬁned the model; he took account of the crystalline orthorhombic symmetry by admixing the Q3 and Q2 deformation modes of ﬁg. 6(a). Recent neutron (Rodríguez-Carvajal et al., 1998) and X-ray (Murakami et al., 1998) diffraction experiments on LaMnO3 have fully corroborated the predicted oxygen displacements with opposite directions of the cooperative displacements in alternate (001) planes (out-of-phase stacking). Mizokawa et al. (1999) have argued that the degeneracy of the direction of oxygen displacements in the (001) planes is lifted by the A–O interactions to give the long-range orbital order in 3D, a larger tilting of the MnO6/2 octahedra (smaller tolerance factor t < 1) favoring in-phase stacking of the oxygen displacements. Kataoka (2001) has extended the theory of Kanamori to include higher-order anharmonic elastic and ﬁrst-order Jahn–Teller energies to account for the ﬁrst-order character of the orbital order–disorder transition at TJT = 750 K. At temperatures T > TJT , the √disordered occupied e orbitals ﬂuctuate to give an O* -orthorhombic symmetry with c/a ≈ 2. Figure 8 shows the variation of the orthorhombic (Pbnm) cell parameters with temperature (Rodríguez-Carvajal et al., 1998). Louca et al. (1997), Egami et al. (1997), and Louca and Egami (1999) have shown with pulsed neutron diffraction and pair-density-function analysis that locally the Jahn–Teller distortions remain on a time scale short compared to 10−12 s where disorder reduces the average distortion viewed on a longer time scale. A Raman scattering study by Granado et al. (2000) also indicates that orbital disorder occurs on heating through TJT and that considerable orbital ﬂuctuation occurs on approaching TJT from below. The apparent loss of ordering of the cooperative MnO6/2 rotation in the O* phase just above TJT is a result of the orbital ﬂuctuations. The cooperative rotations reappear in an O-orthorhombic phase at higher temper-

Fig. 8. Orthorhombic (Pbnm) lattice parameters of LaMnO3 as a function of temperature. The MnO6/2 octahedra become nearly regular in the O* phase (T > TJT ) on the time scale of the measurement, but the displacement parameter of the oxygen atoms increases signiﬁcantly; after Rodríguez-Carvajal et al. (1998).

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¯ rhombohedral structure atures (T > 900 K) before transforming above ca. 1000 K to the R 3c with cooperative rotations about the [111] axis (Zimmermann et al., 2001). Rhombohedral symmetry does not support removal of the e-orbital degeneracy. The type-A antiferromagnetic order of eq. (14) is canted by Dzialoshinksii antisymmetric exchange to give a weak canted-spin ferromagnetic moment oriented along the c-axis (type Ay F z of table 1) (Matsumoto, 1970a); in accordance with table 1, the Dzialoshinskii vector D ij is parallel to the a-axis and the antiferromagnetic component of the Mn-atom spins S = 2 is parallel to the b-axis in space group Pbnm (Zhou and Goodenough, 1999). Cestelli Guidé et al. (2001) have measured with muon spin rotation a cant angle of 2◦ and shown from the critical exponent β of [1 − (T /TN )]β that LaMnO3 is a Heisenberg system near TN with a crossover to Ising behavior at lower temperatures due to magnetocrystalline anisotropy. The Weiss constant of a Curie–Weiss paramagnetic susceptibility is a measure of the sign of the net spin–spin interactions in the paramagnetic state. Figure 9 shows isotropic paramagnetic data for a single crystal of LaMnO3 taken under vacuum (Zhou and Goodenough,

Fig. 9. Magnetic susceptibility χ (T ) and χ −1 (T ) for single-crystal LaMnO3 . χ and χ⊥ could not be resolved in the paramagnetic O phase (TN < T < TJT ), but they are resolved below TN ; after Zhou and Goodenough (1999).

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1999). Early paramagnetic data on a polycrystalline sample showed similar behavior (Jonker and van Santen, 1950). The presence of ferromagnetic interactions within (001) planes and antiferromagnetic interactions between planes in the range TN = 135 K < T < TJT = 750 K gives a Curie–Weiss paramagnetic susceptibility with a positive Weiss constant θ = 52.5 K < TN . The magnetic susceptibility increases discontinuously on increasing the temperature through TJT ; the Curie constant C remains unchanged, but a θ = 177 K > TN for temperatures T > TJT shows that the magnetic interactions become isotropically ferromagnetic where the occupied e orbitals ﬂuctuate. Such a change could be understood as due to the onset of a vibronic superexchange above TJT with no change in the Mn spins provided LaMnO3 remains an insulator at temperatures T > TJT (Goodenough et al., 1961). The resistivity ρ(T ) and thermoelectric power α(T ), obtained under vacuum, of the single crystal of LaMnO3 used in the magnetic study of ﬁg. 9 are shown in ﬁg. 10(a). These measurements (Zhou and Goodenough, 1999) were made both to determine the oxygen stoichiometry of the crystal and to test the assumption that LaMnO3 remains an insulator at temperatures T > TJT . An initial value of α(300 K) ≈ −600 μV/K shows a slight oxygen deﬁciency; on cycling to 1100 K in vacuum, it becomes slightly oxidized to give the α(300 K) ≈ 550 μV/K of

Fig. 10. (a) Resistivity ρ(T ) and thermoelectric power α(T ) taken on cycling a virgin single crystal of LaMnO3 from room temperature to 1100 K measured in a vacuum of 10−3 torr, after Zhou and Goodenough (1999).

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Fig. 10. (b) Optical conductivity spectra for Eab (solid lines) Ec (dashed lines) of a detwinned LaMnO3 crystal at representative temperatures: 10 K, 300 K (TN < T TJT ), 700 K (TN T < TJT ) and 800 K (T > TJT ) after Tobe et al. (2001).

ﬁg. 10(a). The ρ(T ) and α(T ) curves were reversible after the ﬁrst cycle. These data show the sample is oxygen stoichiometric to within 0.1%. Nevertheless, ρ(T ) drops abruptly at TJT to a magnitude comparable to that of a “bad metal” and α(T ) drops to a low, nearly temperatureindependent value. The onset at T ∗ of a sharper decrease in α(T ) and ρ(T ) with increasing temperature in the interval T ∗ < T < TJT correlates with increasing orbital ﬂuctuations on the approach to TJT . The drops in α(T ) and ρ(T ) represent a change from a small to a large fraction of mobile e electrons even though the crystal remains nominally single-valent Mn(III). Given the strong coupling of the e electrons to local lattice deformations below TJT and the observation that dynamic local Jahn–Teller distortions persist above TJT , we may conclude that LaMnO3 is a vibronic conductor above TJT and may have double-exchange as well as vibronic superexchange ferromagnetic interactions. The optical conductivity data of ﬁg. 10(b) show the closing of an energy gap at εF with increasing temperature to TJT , but the absence of a Drude term above TJT that would be present if the conductive electrons were itinerant rather than vibronic. The transition to a conductive state requires the generation of charge carriers and therefore thermal excitations of the disproportionation reaction 2Mn(III) = Mn(II) + Mn(IV).

(22)

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Van Roosmalen and Cordfunke (1994) have analyzed the relation between the partial pressure of oxygen and the value of δ in LaMnO3+δ to conclude that a partial disproportionation reaction is responsible for the surprisingly large oxidation of LaMnO3 in air. This disproportionation reaction accounts for the ready oxidation of LaMnO3 in air, the Mn(II) being oxidized to Mn(III) to give La1−ζ Mn1−ε O3 . In 10−3 torr vacuum, only a small percentage of the Mn(II) are oxidized to give the large α(300 K) > 0; but at T > TJT , the Mn(II) give electronic charge carriers and the Mn(IV) give hole charge carriers of nearly equal concentration, so a temperature-independent α ≈ 0 is found. The fact that the Curie constant C exhibits little change from its value for TN < T < TJT to its value for T > TJT is consistent with a partial charge disproportionation; the observed value of C corresponds to a μeff = 5.2μB , which is to be compared to a spin-only value μeff = 4.9μB for S = 2 and a μeff = 5.0μB for a full disproportionation into Mn(II) with S = 5/2 and Mn(IV) with S = 3/2. Since the disproportionation reaction would be associated with a cooperative breathing-mode deformation that contracts equally the (Mn–O) bond lengths at Mn(IV) and expands equally the (Mn–O) bond lengths at Mn(II), we are led to the conclusion that the cooperative orbital ordering in the O -orthorhombic phase suppresses the disproportionation reaction by localizing the Mn(III) e electrons in the long (Mn–O) bonds within the (001) planes, which hinders breathingmode displacements of the oxygen atoms at the Mn atoms. Although the O -orthorhombic √ (c/a < 2) structure is retained in the interval T ∗ < T < TJT , which indicates the matrix retains occupied e orbitals preferentially ordered into the (001) planes, orbitally disordered ﬂuctuations above T ∗ introduce charge carriers that reduce α(T ), the volume fraction increasing discontinuously at TJT . On raising the temperature through TJT and in the orbitally disordered clusters in the range T ∗ < T < TJT , the locally cooperative oxygen displacements become short range ﬂuctuations in 3D that permit the formation of breathing-mode displacements of some of the Mn atoms. The formation of six short Mn–O bonds creates empty molecular e orbitals at Mn(IV) ions; the six long (Mn–O) bonds stabilize localized Mn(II) : t3 e2 conﬁgurations. The disproportionation reaction may therefore be considered a segregation into localized electrons at Mn(II) and holes delocalized over a Mn(IV)O6/2 cluster as the result of an approach to the condition Uσ ≈ Wσ from the localized electron side. From a theoretical perspective, Ahn and Millis (2001) have used a tight-binding parametrization of band theory and expressions for the elastic energies to argue that the e electrons of LaMnO3 approach the transition to itinerant-electron behavior from the localized-electron side. Moreover, it is apparent from ﬁg. 10(a) that real charge transfer is occurring, which introduces an isotropic, ferromagnetic double-exchange component to the spin–spin coupling. Therefore, some other experiment is required to establish the existence of a vibronic isotropic superexchange interaction. Goodenough et al. (1961) explored the LaMn1−x Gax O3 for this purpose and Lotgering (1970) studied the system La1−x Bax Mn1−x Tix O3 . In each case, all the manganese are Mn(III) and dilution of the Mn(III) by substitution of a non-magnetic ion into the MnO3 array suppresses a static cooperative Jahn–Teller deformation. In each case a ferromagnetic superexchange in an insulator was observed, indicating the presence of a ferromagnetic vibronic superexchange. However, before turning to more recent studies of LaMn1−x Gax O3 and

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LaMn1−x Scx O3 , I draw attention to evidence from high-pressure studies that the σ -bonding e electrons of LaMnO3 approach the transition from localized to itinerant behavior. Millis et al. (1995) proposed on theoretical grounds that the cooperative Jahn–Teller orbital ordering makes LaMnO3 an insulator. This prediction found experimental support in the hightemperature transport measurements of ﬁg. 10(a). Subsequently, Loa et al. (2001) concluded, from their room-temperature structural and reﬂectance data and from resistivity ρ(T ) data all taken to 400 kbar hydrostatic pressure, that (1) the cooperative Jahn–Teller distortion of the Mn(III) octahedra in LaMnO3 disappears at about 180 kbar although the phase remains an O -orthorhombic insulator and, therefore, (2) the insulator behavior of LaMnO3 is not due to the Jahn–Teller orbital ordering. However, the quality of the structural data decreased with increasing pressure, and a closer analysis of their data in comparison with that of PinsardGaudart et al. (2001) shows that these conclusions are not supported by the data. PinsardGaudart et al. (2001) reported room-temperature time-of-ﬂight neutron-diffraction data taken on crushed, oxygen-stoichiometric single-crystal LaMnO3 , a procedure that gave amazingly high-quality diffraction data. These data show that the cooperative Jahn–Teller distortion is stable to about 70 kbar; the reduction with pressure of the different Mn–O bond lengths is nearly the same and the extent of the cooperative MnO6/2 rotations is continuously reduced. Low-temperature measurements revealed that type-A antiferromagnetic order is retained and TN increases as a result of the greater overlap of the Mn-3d and O-2p orbitals. However, a transition to an unknown phase occurred between 70 and 80 kbar. The insulator-metal transition found at about 320 kbar by Loa et al. (2001) is consistent with the theoretical deduction by Ahn and Millis (2001) that the σ -bond e electrons of LaMnO3 approach the transition from localized to itinerant behavior. Pressure experiments (Zhou and Goodenough, 2002a) discussed in sect. 2.7 conﬁrm this deduction. The character of the orbital ordering in the insulator high-pressure phase P 80 kbar has yet to be determined. In order to show that the e-orbital degeneracy is lifted by electron–phonon interactions and not by the superexchange interaction, Allen and Perebeinos (1999) and Perebeinos and Allen (2001) have invoked the Franck–Condon process via self-trapped excitons to predict a Gaussian envelope of vibrational sidebands associated with resonant behavior of a Raman process close to the orbital excitation energy of 2 eV in LaMnO3 . Features of the Raman spectra of LaMnO3 obtained (Björnsson et al., 2000; Romero et al., 2001) for a laser frequency around 1100 cm−1 are consistent with these predictions. In the ﬁrst step of the Raman process, the incident photon excites an electron at a Mn(III) ion from the lower to the upper orbital state of the Jahn–Teller doublet. This orbital exciton (also called an “orbiton”) is selftrapped by oxygen rearrangements from the orbitally ordered Jahn–Teller state, which creates a vibrationally excited state of the orbiton. In the second step of the Raman process, this virtual excitation decays back to the orbital ground state, but not to the vibrational ground state. A number of vibrational quanta are also excited (Franck–Condon principle) to give vibrational sidebands of signiﬁcantly greater magnitude than are found with non-Jahn–Teller ions. Perebeinos and Allen (2000) have also predicted that the vibrational quanta associated with a photoexcited hole in a photoemission experiment are responsible for a ca. 0.5 eV broadening observed in angle-resolved photoemission spectra of the manganese-oxide perovskites (Dessau and Shen, 1998).

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If the orbital exciton is not self-trapped by interactions with oxygen optical-mode vibrations, then it may propagate through the crystal as an orbital wave since there is inertia to slow restoration to the ground state (Ishihara et al., 1997). A quantized orbital wave is a new particle, the itinerant orbiton, analogous to the magnon corresponding to a quantized spin wave. The spin waves in a ferromagnetic crystal are detected by changes in the properties of a beam of photons or neutrons that is scattered from a single crystal. Saitoh et al. (2001) have used Raman scattering from a high-quality LaMnO3 single crystal to detect a frequency shift that weakens as the temperature is increased from 9 K until it completely disappears above TJT . They interpret this shift to be due to the presence of orbital-wave orbitons, but Allen and Perebeinos (2001) cautioned that the theory needs to introduce orbiton–phonon interactions before this demonstration can be considered “air tight”. Subsequently, van den Brink (2001) has developed a theory that introduces the electron–electron correlations and lattice dynamics on the same footing. His analysis accounts for the data of Saitoh et al. (2001) with a relatively weak electron–phonon coupling that, nevertheless, narrows the itinerant orbiton dispersion by a factor of two. The theory of Allen and Perebeinos applies to the strong-coupling limit. Orbitons may inﬂuence other physical properties such as heat capacity or thermal conductivity. Measurements (Tobe et al., 2001; Quijada et al., 2001) of the optical-conductivity spectra of detwined single crystals of LaMnO3 from 10 K < TN to 300 K > TN have shown a pronounced difference in the lowest-lying 2 eV excitation for the electric ﬁeld Eab and Ec (Pbnm setting) that changed little on crossing TN , but decreased gradually with increasing temperature to TJT across which it collapsed. The fact that the anisotropy reﬂects the orbital ordering and not the spin ordering indicates a large O-2p admixture in the Mn(IV)/Mn(III) redox couple to facilitate an allowed 2p–3d transition. Quijada et al. (2001) interpret the 2 eV excitation to be the interatomic Mn(III) + Mn(III) = Mn(IV) + Mn(II) e–e transition rather than the intraatomic transition examined by Allen and Perebeinos (1999). 2.2. LaMn1−x Gax O3 and LaMn1−x Scx O3 Reexamination (Töpfer and Goodenough, 1997a) of the insulator system LaMn1−x Gax O3 with oxygen-stoichiometric samples conﬁrmed the earlier study √ (Goodenough et al., 1961) in this system. As shown in ﬁg. 11, √ the O -orthorhombic c/a < 2 phase is retained to x = 0.5, albeit with a c/a approaching 2 monotonically with increasing x; long-range orbital order is retained in a percolating matrix to x = 0.5. However, the saturation magnetization at 4 K approaches the spin-only value of 4μB /Mn for x 0.5. Moreover, the Néel temperature TN of the canted-spin, type-A antiferromagnetic order decreases with dilution of the Mn concentration to x = 0.25; the magnetic-ordering temperature increases to a higher ferromagnetic Curie temperature TC at x ≈ 0.30 that decreases monotonically with increasing x. Moreover, in a ﬁeld of 100 Oe the paramagnetic Weiss constant θ increases with x, changing from θ TN for x 0.20 to a θ > TN for x 0.30. The magnetization data for these polycrystalline samples prompted a closer look with an oxygen-stoichiometric series of single-crystal samples in the range 0.15 x 0.50 (Zhou et al., 2001a). The zero-ﬁeld-cooled (ZFC) and ﬁeld-cooled (FC) magnetization M(T ) under applied ﬁelds of 10 Oe, 50 Oe, and 5 kOe as well as the reciprocal magnetization M −1 (T )

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Fig. 11. Variation with x of the magnetic moment per Mn ion in Bohr magnetons at 4 K (straight line represents ferromagnetic spin-only value) and magneticordering temperatures (crossed circles) for LaMn1−x Gax O3 , after Goodenough et al. (1961).

in 5 kOe are shown in ﬁg. 12 for x = 0.15, 0.25, 0.35, and 0.50 samples. Whereas the curves for x = 0.15 and 0.25 are typical of a type-A canted-spin antiferromagnet having a θ > 0 because of the ferromagnetic exchange interactions in the basal planes, the low-ﬁeld M(T ) curves for x = 0.35 and 0.50 show a maximum in the ZFC curves near the magnetic-ordering temperature, which is typical of a spin glass (Mydosh, 1993). An ac susceptibility χac (T ) of the x = 0.5 crystal is also plotted; it shows a sharp peak at the spin-freezing temperature Tf . On the other hand, the M(T ) curve taken in 5 kOe is typical of a ferromagnet with a TC ≈ Tf . Since a saturation spin-only moment of 4μB /Mn is achieved in single-crystal samples under an applied ﬁeld of only a few kOe (ﬁg. 13) and the hysteresis loop has a small remanence, it is apparent that a modest magnetic ﬁeld induces a transition from a spin glass to a ferromagnetic phase in the x = 0.5 sample. From the inset of ﬁg. 13, this transition is initiated at about H = 2500 Oe; the volume fraction of the ferromagnetic phase increases with H , saturating at H 2 kOe. The data of ﬁg. 11 show that for x > 0.5 the system has the O* -orthorhombic structure indicative of orbital disorder in zero ﬁeld; these polycrystalline samples are ferromagnetic with a saturation magnetization at 4 K approaching 4μB /Mn atom. Since the O -orthorhombic phase is retained in zero ﬁeld at x 0.5, these results have a straightforward interpretation. In zero ﬁeld, an orbitally ordered, antiferromagnetic matrix with Néel temperature TN percolates through the structure if x 0.5; but orbitally disordered, ferromagnetic clusters are present in the matrix for x 0.30, and these clusters have a TC > TN . The application of a magnetic ﬁeld stabilizes the orbitally disordered ferromagnetic phase relative to the orbitally ordered antiferromagnetic phase, and the ferromagnetic clusters grow in a magnetic ﬁeld at the expense of the antiferromagnetic matrix. In this system, there is no negative magnetoresistance associated with the growth of the ferromagnetic clusters to beyond their percolation threshold; the orbitally disordered phase remains insulating for larger values of x. On the other hand, ap-

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Fig. 12. The temperature dependence of the magnetization M(T ) and its reciprocal M −1 (T ) under different applied ﬁelds for single crystals of the system LaMn1−x Gax O3 . The ac susceptibility χac (T ) of the x = 0.5 sample is superimposed, after Zhou et al. (2001a).

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Fig. 13. The magnetization vs. applied magnetic ﬁeld at T = 5 K for single-crystal samples of the LaMn1−x Gax O3 system. The full hysteresis loop is shown for the x = 0.5 sample; the inset is the detail in low ﬁelds, after Zhou et al. (2001a).

plication of hydrostatic pressure appears to stabilize the orbitally ordered matrix, which has a smaller volume (Zhou et al., 2001a). A zero-ﬁeld phase diagram for the LaMn1−x Gax O3 system is shown in ﬁg. 14. Four important conclusions follow from the studies made of this system: (1) An isotropic ferromagnetic, vibronic Mn(III)–O–Mn(III) superexchange interaction is found where the occupied e orbitals ﬂuctuate. (2) A magnetic ﬁeld stabilizes the orbitally ﬂuctuating, ferromagnetic phase relative to the orbitally ordered antiferromagnetic phase; and where the two phases coexist, a magnetic ﬁeld may induce a transition from a spin-glass to a ferromagnetic phase. (3) The σ -bonding e electrons of the Mn(III) ions remain localized in the orbitally ﬂuctuating state where Ga substitutions perturb the periodic potential of the MnO3 array. (4) Hydrostatic pressure stabilizes an ordering of the occupied e orbitals that decreases the volume fraction of disordered orbitals. For comparison, Al(III) and Sc(III) were substituted for Mn(III) (Goodenough et al., 2002). These ions also perturb the periodic potential of the MO3 array to maintain localized e electrons at the Mn(III) ions where the orbitals become disordered. In these solid-solution

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Fig. 14. Phase diagram for the LaMn1−x Gax O3 as obtained with single-crystal samples, after Goodenough et al. (2002).

systems also, the disproportionation reaction 2Mn(III) = Mn(II) + Mn(IV) is suppressed. Single-phase LaMn1−x Alx O3 was restricted to the range 0 x 0.20 where it remained a canted-spin antiferromagnet. On the other hand, single-phase LaMn1−x Scx O3 was found over the entire √ range of solid √ solutions 0 x 1. This√system showed a smooth crossover from c/a < 2 to c/a > 2 near x = 0.35; c/a > 2 became independent of x above x = 0.75. The Sc(III) ion is larger and has a stronger octahedral-site preference than Ga(III), which makes Sc(III) more resistant to the cooperative Jahn–Teller distortion induced by the Mn(III) ions. The smaller Al(III) ion, on the other hand, offers little resistance to a cooperative Jahn–Teller distortion, and the c/a ratio changed little in the range 0 x 0.20 of LaMn1−x Alx O3 . The phase diagram of ﬁg. 15 for LaMn1−x Scx O3 shows an evolution with x from cantedspin antiferromagnetic insulator (CAFI) to spin-glass insulator (SGI) to ferromagnetic insulator (FI) that is similar to that of the LaMn1−x Gax O3 system. Moreover, the spin-glass phase transforms to a ferromagnetic phase in a high magnetic ﬁeld; the evolution with x of the magnetization at 5 K in a ﬁeld of 50 kOe is shown in ﬁg. 16. In polycrystalline LaMn1−x Scx O3 , as in polycrystalline LaMn1−x Gax O3 , the full theoretical spin-only moment of 4μB /Mn is not attained for any value of x whereas the full moment was found in the single crystals of LaMn1−x Gax O3 . The evolution of the magnetic ordering temperature indicates that spin-glass behavior is found where the ferromagnetic clusters within the antiferromagnetic matrix have a TC > TN . The more rapid drop-off in TN with x as x approaches the critical value xc ≈ 0.30 where TN = Tf ≈ TC shows the presence of orbitally disordered clusters appearing for x < xc ;

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Fig. 15. Phase diagram for the LaMn1−x Scx O3 system as obtained with polycrystalline samples, after Goodenough et al. (2002).

Fig. 16. The magnetization at 50 kOe vs. x at T = 5 K for LaMn1−x Scx O3 , after Goodenough et al. (2002).

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the clusters dilute the antiferromagnetic matrix more rapidly than a simple substitution of Sc(III) ions. 2.3. RMnO3 The stoichiometric manganites RMnO3 with larger lanthanide ions La to Dy all form the O orthorhombic Pbnm structure at room temperature while those with the smaller lanthanide ions Ho to Lu or with Y all take the hexagonal P63 cm structure of ﬁg. 17. High-resolution electron diffraction taken on single crystals of RMnO3 (R = Y, Yb, Lu) have demonstrated the formation of Mn trimers within the MnO ab planes as well as a ferroelectric distortion along the c-axis in the hexagonal structure (Katsufuji et al., 2001). Long-range magnetic order is frustrated by competing exchange interactions in the MnO planes, which lowers TN and sustains spin ﬂuctuations well below TN . However, an O -orthorhombic perovskite form of RMnO3 for the smaller rare-earth ions can be prepared either by high pressure (Wood et al., 1973) or from citrate-based precursors (Szabo, 1969), which has allowed study of the entire RMnO3 series of perovskite manganites (Szabo, 1969; Quezel-Ambrunat, 1968; RodríguezCarvajal et al., 1998; Troyanchuk et al., 1997; Quezel et al., 1974, 1977; Jirák et al., 1997; Matsumoto, 1970b; Brinks et al., 2001). The cooperative rotations of the MnO6/2 octahedra increase with decreasing radius of the R3+ ion, i.e., with decreasing tolerance factor t. As the bending angle φ of the (180◦ − φ) Mn–O–Mn interactions increases, the strength of the ferromagnetic σ -bond superexchange in the (001) planes is weakened relative to that of the antiferromagnetic t3 –O–t3 interactions. As a result, the Néel temperature TN for ordering of the manganese moments decreases systematically from 141 K for R = La to 50 K for R = Eu; and for R = Tb, Ho, and Y the ferromagnetic (001) planes transform to an incommensurate spiral-spin conﬁguration propagating along the b-axis in the bc plane, see ﬁg. 18, with a TN ≈ 40 K. The propagation vector k = ky b∗ increases with decreasing ionic radius of the R3+ ion. In orthorhombic HoMnO3 , it also in-

Fig. 17. Hexagonal P63 cm structure of LuMnO3 , after Katsufuji et al. (2001).

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Fig. 18. The magnetic ordering of Mn(III)-ion spins in RMnO3 , R = La, Pr, Nd, Tb, Ho (and Y), in two adjacent (001) planes. Not shown is the spin canting to give a small ferromagnetic component along the c-axis for R = La, Pr, Nd. The numerical values refer to the spin periodicity just below TN , after Brinks et al. (2001).

creases with decreasing temperature from 0.395b∗ just below TN to 0.431b∗ at THo = 11 K, the ordering temperature of the Ho3+ -ion moments. A dt/dT > 0 means that t decreases with temperature as well as with substitution of smaller A cations. The Ho3+ moments order in a spiral-spin conﬁguration with the same propagation vector k as that of the Mn(III) spins. At lowest temperatures, a commensurate spiral-spin conﬁguration coexists with the incommensurate conﬁguration (Brinks et al., 2001). 2.4. CaMnO3 Oxygen-stoichiometric CaMnO3 can be prepared in a ﬂowing O2 atmosphere; at room tem√ perature, it has the O-orthorhombic (c/a > 2) perovskite structure. The half-ﬁlled t orbitals of the Mn(IV) : t3 e0 ions give rise to antiferromagnetic t3 –O–t3 superexchange interactions between all nearest neighbors. As there are no other competitive interactions, CaMnO3 is a type G (see table 1) antiferromagnetic insulator with a Néel temperature TN = 125 K and a spin-only paramagnetic moment μeff = 3.9μB ; the atomic moment of the antiferromagnetic state, μMn ≈ 2.64μB (Yudin et al., 1966) is reduced from 3.0μB by the virtual charge transfer of the antiferromagnetic superexchange interaction. One remarkable feature of this compound is an anomalously low thermal conductivity κ(T ) in the paramagnetic phase; κ(T ) increases abruptly on cooling through TN (Fujishiro et al., 2000; Zhou and Goodenough, 2002b). Since CaMnO3 is an insulator, only the magnons and phonons contribute to κ(T ); therefore, the κ(T ) data indicate that spin disorder suppresses not only the magnons, but also the phonons. Since the orbital angular momentum is quenched in a t3 e0 conﬁguration and there are no orbital ﬂuctuations, the spin-lattice interactions would appear to be due to an exchange striction, antiferromagnetic coupling on opposite sides of an oxygen atom giving rise to shorter Mn–O bond lengths. In the paramagnetic phase, random exchange-strictive displacements would perturb the periodicity of the lattice and suppress the optical phonons. However, the superexchange interaction, eq. (9), involves a virtual charge transfer between cations that does not alter the Mn–O equilibrium bond length. Therefore, we

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need to introduce the semicovalent-exchange component that was ﬁrst introduced by Goodenough (1963), who showed it gave the same sign of the exchange coupling. Subsequently, it was given analytic form by Geertsma (1979) and quoted by Zaanen and Sawatzky (1987). This interaction involves a two-electron virtual charge transfer from the intermediate oxygen, one of one spin to one side and one of opposite spin to the other side. Each electron transfer costs an energy Δ if the on-site electrostatic energy for the oxygen 2p electrons is small, i.e., Upp Δ. Addition of the semicovalent exchange component changes the expression for the superexchange interaction from that given in eq. (9) to 2|b ca|4 (23) (1/Ueff + 1/2Δ), Δ2 where the ﬁrst term is just the Anderson superexchange term in which bij ∼ Δ2 λ4π with λπ = bca /Δ and bca is the cation–anion resonance (electron-energy transfer) integral. The second term in eq. (23) is the semicovalent-exchange component. Where the highest occupied redox couple in the point-charge model of an ionic crystal lies below the O2− : 2p6 level, a Δ < Ueff makes the semicovalent exchange larger than the Anderson component of the superexchange interaction. A two-electron transfer from the oxygen, one to each of its neighboring Mn atoms, would increase Mn–O–Mn bonding where the Mn-atom spins on opposite sides of the oxygen are antiparallel. Accordingly, an important exchange-strictive contraction of the Mn–O bond lengths occurs on cooling through TN (Moritomo et al., 2001). In order to test whether the semicovalent exchange striction is responsible for the surprising suppression of κ(T ) in the paramagnetic phase of CaMnO3 , the κ(T ) of single-crystal CaMnO3 was compared to that for single-crystal LaMnO3 , LaGaO3 , large-grained YCrO3 , and SmNiO3 (Zhou and Goodenough, 2002b). The reciprocal thermal conductivity κ −1 (T ) is plotted for these compounds in ﬁg. 19 where the dotted line represents that of an oxide glass. As expected, LaGaO3 has a normal κ(T ) behavior whereas κ(T ) is suppressed in the paramagnetic phase of the four antiferromagnetic compounds; the suppression increases progressively on going from YCrO3 to LaMnO3 to CaMnO3 to SmNiO3 . This progression correlates with the magnitude of the charge-transfer gap Δ from the O-2p bands to the lowest unoccupied redox energy of the transition-metal atoms, as can be seen from the schematic energy diagrams of ﬁg. 20. This experiment provides a conﬁrmation of the competitive character of the semicovalent exchange component of the superexchange interaction. Jij ∼

2.5. SrMnO3 SrMnO3 has a tolerance factor t > 1, which places the Mn–O–Mn bonds under tension and the Sr–O bonds under compression. These stresses are relieved by the formation of hexagonal polytypes (Goodenough et al., 1972). SrMnO3 forms the 6H hexagonal polytype in which the (111) close-packed SrO3 planes of the cubic structure have hexagonal stacking alternating with two cubic stackings instead of all-cubic stacking. Alternatively, loss of oxygen reduces some of the manganese to Mn(III), thereby increasing the mean ionic radius of the manganese ions to reduce t and stabilize the cubic phase. Oxygen-deﬁcient, cubic SrMnO3−δ is a mixed oxide-ion/electron conductor, but in air it picks up oxygen above 600 ◦ C to revert to the hexagonal polytype (Tichy and Goodenough, 2002).

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Fig. 19. Thermal conductivity κ(T ) and its inverse of single-crystal LaGaO3 (LGO), LaMnO3 (LMO), CaMnO3 (CMO), and large grained YCrO3 (YCO). The dotted line is that of an oxide glass. The arrows indicate the Néel temperatures TN , after Zhou and Goodenough (2002b).

2.6. Sr1−x Cax MnO3 (0 x 1) and Sr1−y Bay MnO3 (0 y 0.2) According to eqs. (7) and (9), the Néel temperature TN of the system Sr1−x Cax MnO3 and Sr1−y Bay MnO3 should increase with increasing x and y as cos2 θ increases with the tolerance factor t; θ = (180 ◦ − φ) is the Mn–O–Mn bond angle. Neumeier et al. (2001) have shown that the transition at TN in CaMnO3 is second-order with a jump in the speciﬁc heat ΔCp = −9.9 ± 0.7 J/mol at TN = 124.2 K. Chmaissem et al. (2001) obtained TN and, with neutron and synchrotron X-ray powder diffraction, the values of cos2 θ as a function of x and y. The system Sr1−x Cax MnO3 is O-orthorhombic (Pbnm) for 0.4 < x 1.0, tetragonal ¯ for 0 x 0.3; Sr1−y Bay MnO3 is cubic for (I4/mcm) for 0.3 x 0.4, and cubic (Pm3m) all values of y 0.2 obtained at lower temperatures under a high oxygen pressure. As shown in ﬁg. 21, Chmaissem et al. (2001) found experimentally the relationship

TN θ, σ 2 = TN,max (180◦, 0) − C1 1 − cos2 θ − C2 σ 2 , (24) where C1 and C2 are constants and σ 2 ≡ (rA0 − rA )2 is the variance of the room-temperature ionic radii associated with different A-site cations; rA0 is the radius of Sr2+ obtained from cubic SrMnO3 . To ﬁt the experimental variation of TN with x and y, it was necessary to add the term C2 σ 2 to take account of the variation in the periodic potential as a result of changes in θ induced by different A-site cations bonding with the bridging oxygen atoms.

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(a)

(b)

(c)

Fig. 20. (a) Schematic energy diagrams for YCrO3 , LaMnO3 , and CaMnO3 . (b) The charge transfer gap Δ measured by optical spectra, after Arima et al. (1993). (c) Virtual electron transfers for 180◦ t3 e0 –O–t3 e0 in Anderson superexchange and semicovalent exchange. In Anderson superexchange, the operative transfer integrals are between the crystal-ﬁeld orbitals ψt = Nπ (ft − λπ φπ ), after Zhou and Goodenough (2002b).

2.7. Bloch’s rule Bloch (1966) studied the variation of the Néel temperature TN with volume V for numerous antiferromagnetic insulators and found the general relationship αB ≡ d log TN /d log V ≈ −3.3 ± 0.4.

(25)

This relationship, known as Bloch’s rule, applies in the localized-electron limit where the interatomic spin–spin interaction is described by the superexchange perturbation theory of eq. (23) with TN ∼ J ; J is the Heisenberg exchange energy. Calculations by Shrivastava and

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(a)

(b)

Fig. 21. (a) Observed (ﬁlled circles) and calculated (open circles) TN as a function of rA . (b) Calculated TN values (open circles) obtained by subtracting the individual contributions of C1 [1 − cos2 θ ] (ﬁlled squares) and C2 σ 2 (ﬁlled triangles) from TN,max = 233 K (see eq. (24)), after Chmaissem et al. (2001).

Jaccarino (1976) and by Smith (1969) have given a bca ∼ r −n with n ≈ 2.5–3.0 for an equilibrium M–O bond length r. If U and Δ of eq. (23) are pressure-independent, it follows that TN ∼ r −10 ∼ V −3.3 . If the compressibility K ≡ −V −1 ∂V /∂P remains constant, the pressure dependence of TN should conform to Bloch’s rule. Therefore, any deviation from Bloch’s rule would be an indication that either the superexchange perturbation approach breaks down or the assumption that U and Δ are pressure-independent is not valid. A determination of αB for LaMnO3 and CaMnO3 has been compared to αB for YCrO3 (Zhou and Goodenough, 2002a). Figure 22 compares TN vs. hydrostatic pressure P for these three compounds. The data for LaMnO3 is non-linear below 7 kbar; a ﬁrst-order phase change at 7 kbar is followed by an unusually large slope dTN /dP = 0.55 K/kbar for P > 7 kbar, which is to be compared to a dTN /dP = 0.34 K/kbar for CaMnO3 and 0.30 K/kbar for YCrO3 over the entire pressure range. A neutron-diffraction study to 70 kbar by PinsardGaudart et al. (2001) has shown retention over the entire pressure range of the cooperative ordering of the e electrons into the (001) planes and a compressibility K = 0.70 × 10−6 /bar

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Fig. 22. Pressure dependence of TN for LaMnO3 , CaMnO3 , and YCrO3 . Straight lines are linear ﬁttings of the data, after Zhou and Goodenough (2002a).

that is comparable to the K = 0.68 × 10−6/bar found by Bloch (1966) for other antiferromagnetic insulators. A measured |αB | = 5.3 for LaMnO3 under P > 7 kbar is to be compared with eq. (25) and an estimated (assuming K = 0.68 × 10−6 /bar) |αB | = 3.8 and 3.0 for CaMnO3 and YCrO3 , respectively. YCrO3 clearly obeys the Bloch rule and CaMnO3 is at its upper limit, but LaMnO3 has an unusually large |αB | in the range P > 7 kbar as well as an anomalous dTN /dP in the range P < 7 kbar and a two-phase region at P ≈ 7 kbar. In YCrO3 and CaMnO3 , the t3 –O–t3 interactions contain an effective on-site energy Uπ that is augmented by the intraatomic exchange energy Δex > 2.5 eV whereas the Uσ for the e1 – O–e0 interactions in the (001) planes of LaMnO3 is not augmented and is too small to inhibit a disproportionation reaction above TJT . Moreover, the anomalous behavior of dTN /dP in LaMnO3 cannot be attributed to either an orbital reorientation or an anomalous compressibility. Therefore, we conclude there is a breakdown of the perturbative description of the spin– spin interactions in the (001) planes and/or the assumption that the factor [Uσ−1 + (2Δ)−1 ] in eq. (23) is pressure-independent. Such a breakdown would occur on the approach to the transition from localized-electron to band magnetism. The on-site energy U collapses due to screening in the band regime where the bandwidth is W > U . This collapse at crossover is relatively sharp because the screening is feedback-enhanced on the approach to the localized

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Fig. 23. Schematic energy diagram of the Heisenberg exchange energy J vs. bandwidth W at the crossover from localized-electron to band magnetism, after Zhou and Goodenough (2002a).

to itinerant electronic transition. Moreover, from the virial theorem of eq. (19), we can expect a double-well potential for the equilibrium M–O bondlength at crossover and therefore a ﬁrstorder phase change with a spinodal phase segregation. In perovskite-related oxides, such spinodal phase segregations set in near room temperature, which is too low for atomic diffusion. Therefore, phase segregations on a small length scale are generated by atomic displacements that give rise to either static charge-density waves or to bond-length ﬂuctuations and dynamic phase segregation. A dTN /dP < 0 is predicted for band antiferromagnetism; it has been conﬁrmed in CaCrO3 (Goodenough et al., 1968). Therefore, we place the exchange interaction J for the (001) planes of LaMnO3 at the approach to the crossover from localized-electron to band magnetism where Uσ is decreasing with pressure because of a feedback enhanced screening; the ﬁrst-order phase change at P ≈ 7 kbar suggests a spinodal phase segregation into localized-electron and itinerant-electron antiferromagnetism under pressures P > 7 kbar as indicated in the schematic J vs. W diagram of ﬁg. 23.

3. Mixed-valent perovskites 3.1. Oxygen vacancies CaMnO3 catalyzes the selective oxidation of hydrocarbons by accepting electrons into the MnO3 array during a dissociative chemisorption of the reactant and then releasing oxygen to the departing species. Each oxygen vacancy captures the two electrons it introduces on the two neighboring, ﬁvefold-coordinated Mn(III) ions. The square-pyramidal conﬁguration of the Mn(III) ions was ﬁrst detected by Poeppelmeier et al. (1982a) in polycrystalline CaMnO2.5 that was obtained (Poeppelmeier et al., 1982b) by reaction of CaMnO3 in a 10% H2 /He atmosphere within the narrow temperature interval of 300–325 ◦ C. Reller et al. (1984) subsequently demonstrated the existence of several vacancy-ordered intermediate phases in the interval 0 δ 0.5, all of which have the structural conﬁguration of two squarepyramidal Mn(III) ions trapped at opposite sides of an oxygen vacancy. Wiebe et al. (2001) showed that CaMnO2.94 retains the G-type antiferromagnetic order of CaMnO3 below TN with

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μMn = 2.43μB ; the reduction of μMn from the spin-only moment of 3.0μB reﬂects the virtual electron transfers of the Mn–O–Mn superexchange interactions. Evidence of a vacancyordered phase coexisting with a G-type antiferromagnetic spin conﬁguration was found in a CaMnO2.89 sample; the Mn(III)––Mn(III) e1 ––e1 superexchange interaction is antiferromagnetic, and the single Mn(III)–O–Mn(IV) e1 –O–e0 interaction on the opposite side does not provide a strong enough ferromagnetic coupling to overcome the six nearest-neighbor antiferromagnetic t3 –O–t3 interactions at the Mn(IV) ion. 3.2. Ca1−x Lax MnO3 , 0 x 0.2 Lanthanum substitution for Ca in Ca1−x Lax MnO3, 0 x 0.2, has been used to introduce electrons into the MnO3 array while keeping it intact. Each La3+ ion creates a shallow donor level below the Mn(IV)/Mn(III) redox level; at lowest temperatures, the electrons are trapped at one (or more) of the eight Mn nearest neighbors of a La3+ ion. Neumeier and Cohn (2000) have correlated the electronic resistivity ρ(T ) with Ms (0), the saturation magnetization at T = 0 K (extrapolated from 5 K). They distinguished four compositional regions in the interval 0 x 0.2. Region I (0 < x < 0.02) contains small-polaron Mn(III) ions that increase the saturation magnetization by dMs (0)/dx = 1.20 ± 0.25μB/Mn. Region II (0.02 < x 0.07) contains two-manganese (Zener) polarons and a dMs (0)/dx = 8.4 ± 0.35μB/Mn. Ms (0) reaches a maximum in the interval 0.07 < x < 0.08, and Region III (0.08 < x < 0.17) shows a dMs (0)/dx ≈ −4.5μB /Mn. Region IV (0.18 x 0.20) is a C-type (table 1) antiferromagnet with Ms (0) = 0μB /Mn. At low temperatures (50 K < T < 150 K), the n-type resistivity ρ(T ) ∼ exp(−Ea /kT) had an Ea ≈ 85 meV for x = 0, an Ea ≈ 30 meV independent of x in the interval 0.005 x 0.10, and an Ea ≈ 85 to 95 meV for 0.12 x 0.20. For T > 200 K, the ρ(T ) curves resembled those of a degenerate semiconductor with variable range hopping below a mobility edge. Interpretation by Neumeier and Cohn (2000) of the changes in Ms (0) with x was as follows: The small polarons are coupled antiparallel to their nearest neighbors, retaining the G-type antiferromagnetic order, but the e electrons are sufﬁciently mobile below TN to move to the spin sublattice parallel to the magnetizing ﬁeld. This model gives a weak ferrimagnetism with a dMs (0)/dx = 1μB /Mn. The e1 –O–e0 ferromagnetic interactions do not dominate the antiferromagnetic t3 –O–t3 interactions in this case. On the other hand, Zener polarons have fast (τh < ωo−1 ) e-electron transfer between the Mn(III) and Mn(IV) ions of the pair, which introduces two-manganese ferromagnetic clusters via intrapolaron double exchange. If all the electrons formed Zener polarons, Ms (0) would vary with x as dMs (0)/dx ≈ 7μB /Mn for spinonly moments to give Ms (0) = 0.5μB /Mn at x = 0.07 instead of the observed 0.4μB /Mn. It follows that the electrons initially introduced (0 < x 0.02) form small polarons; but as x increases, they are progressively transformed into Zener polarons. The activation energy for electron transport by a Zener polaron is smaller than that for a small polaron (0.30 meV vs. 0.85 meV). In the interval 0.08 < x < 0.17, the electrons segregate into an electronrich C-type antiferromagnetic phase with no Dzialoshinskii spin canting and an electronpoor phase dominated by small-polaron conduction. Trapping of the Zener polarons in the C-type antiferromagnetic phase causes the resistivity at 5 K, which is a minimum in the range

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0.07 x 0.1, to increase by over ﬁve orders of magnitude as x increases in the range 0.10 < x 0.20. In the C-type antiferromagnetic order, ferromagnetic c-axis chains are coupled antiparallel to one another, and the e electrons occupy (3z2-r2 ) orbitals oriented along the c axis, which inhibits their mobility in 3D. The e electrons probably form a 1D charge-density wave propagating along the c-axis. Granado et al. (2001) have reported an anomalous softening of the bending modes and hardening of the stretching mode of the oxygen vibrations on cooling through TN ≈ 120 K in CaMnO3 and a complete suppression of the frequency shift on cooling through TN after doping with only 3% La in La0.03Ca0.97 MnO3 . The anomalous frequency shift was attributed to a spin–phonon coupling that is dramatically weakened by the introduction of Mn(III), but the origin of the spin–phonon coupling and its suppression were not identiﬁed. We attribute the frequency shift to the suppression of phonons in the paramagnetic phase and the appearance of phonons in the antiferromagnetically ordered phase. As discussed above, local exchangestrictive atomic displacements in the paramagnetic phase appear to be induced by the semicovalent component of the superexchange interactions; random atomic displacements were seen to suppress the phonon contribution to the thermal conductivity, ﬁg. 19. Below TN , the phonon and/or magnon contributions to κ(T ) are restored. A similar phenomenon was found in LaMnO3. However, the system LaMn1−x Gax O3 shows a systematic decrease with x in the phonon contribution to κ(T ) below TN , ﬁg. 24, as a result of the bond-length ﬂuctuations associated with orbital ﬂuctuations at some of the Mn(III) ions. A similar phenomenon would occur in lightly doped Ca1−x Lax MnO3 ; the occupied e orbitals at the Mn(III) ions ﬂuctuate for x 0.07 so as to introduce bond-length ﬂuctuations that suppress the formation of phonons below TN and therefore any frequency shift of the oxygen vibrational modes due to phonon formation on cooling through TN .

Fig. 24. Temperature dependence of the thermal conductivity κ for single-crystal samples of LaMn1−x Gax O3 . The arrows mark TN or Tf obtained from measurement of the magnetic susceptibility, after Zhou et al. (2001a).

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Moritomo et al. (2001) have conﬁrmed the drop in polaron activation energy with electron doping in the range 0 < x 0.10 and the existence of a remarkable increase with x in Ms (0) in the range 0.05 < x < 0.08; they also found the jump ΔC of the lambda anomaly in the speciﬁc heat at TN was ΔC ≈ 1.4k (k = Boltzmann constant) in the range 0 x 0.03 and increased linearly with x to ΔC ≈ 2.3k in the range 0.04 x 0.08. It thus appears that the ferrimagnetic order for small polarons gives an Ising behavior below TN (ΔC = 1.5k) whereas the spin glass regions associated with Zener polarons give a Heisenberg behavior below TN (ΔC = 2.2k). A theoretical model (Chen and Allen, 2001) of the lightly electron-doped MnO3 array of CaMnO3 found bipolaron formation unstable, phase separation unlikely, small polarons trapped in seven-manganese clusters for x < 0.045, and a transition to metallic behavior at x ≈ 0.045. The seven-manganese clusters consisted of a central Mn(III) ion and the six nearest-neighbor Mn(IV) with ﬂuctuations of the occupied (3z2 -r2 ) orbital on the Mn(III) ion between the three (180◦ − φ) O–Mn–O bond axes. Experimentally, the formation of Zener polarons having a small motional enthalpy develops in the interval 0.02 < x < 0.07 in place of a global transition to itinerant-electron behavior at temperatures T < 150 K. Phase segregation in the interval 0.08 < x < 0.18 appears to be a result of ordering of the axes of the Zener two-manganese polarons along the c-axis. 3.3. LaMnO3+δ Early attempts to prepare the perovskite LaMnO3 showed that it becomes oxidized on reaction in air. Although the oxidized compound is conveniently characterized as LaMnO3+δ , its structural formula is La1−ζ Mn1−ε O3 (ζ > ε) since the perovskite structure does not accept interstitial oxygen and tolerates A-cation vacancies more readily than Mn-cation vacancies. Experimentally, the ratio O/Mn = 3 + δ is determined chemically, and the fraction of cation sites that are vacant to give 2δ Mn(IV) is (ε + ζ ) ≈ 2δ/3. Of interest is the evolution of physical properties across the transition from a spin-canted antiferromagnet with small-polaron charge carriers to a ferromagnetic metal via a mixed ferromagnet/antiferromagnet in the interval 0 δ 0.21, where δ = 0.21 approaches the oxidation limit. As shown in ﬁg. 25, √ there is a ﬁrst-order transition at room temperature from an O ¯ perovskite across the interval orthorhombic (c/a < 2) perovskite to a rhombohedral R 3c 0.05 < δ < 0.10. The O structure signals retention of cooperative Jahn–Teller Mn(III)-site distortions that order the occupied e orbitals into the (001) planes to give the canted-spin A-type antiferromagnetic order of the parent compound LaMnO3 . With the antiferromagnetic component of the spins along the b-axis (Pbnm axes) and a Dzialoshinskii vector along the a-axis, a weak ferromagnetic component is along the c-axis (see table 1). The introduction of Mn(IV) ions leaves unchanged the antiferromagnetic t3 –O–t3 interactions between the ferromagnetic (001) planes. Within the (001) planes, Mn(IV) ions may create 2D orbital ﬂuctuations and/or formation of two-manganese Zener polarons without disrupting the A-type antiferromagnetic order. On the other hand, rhombohedral symmetry does not remove the e-orbital degeneracy, and this structure is generally associated with itinerant e electrons and therefore with ferromagnetic metallic behavior via de Gennes double exchange. The coexistence of two electronic phases at the crossover from localized to itinerant electronic behavior

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Fig. 25. Variation with δ of room-temperature lattice parameters of LaMnO3+δ , after Töpfer and Goodenough (1997b).

in the oxides with perovskite-related structures is a recurring theme. In order to investigate how the character of the mobile charge carriers and the magnetic order change on traversing the compositional range of the structural phase change, systematic transport and structural studies were made over the range 0.08 δ 0.18 (Töpfer et al., 1996; Töpfer and Goodenough, 1997b). The changes encountered in this system are to be compared with those found in the system La1−x Srx MnO3 in sect. 3.5. At higher temperatures, 700–1000 K, a positive thermoelectric power α(T ) is essentially temperature-independent and the evolution of its magnitude with δ is consistent with polaronic conduction described by the statistical component

α = (k/e) ln β(1 − c)/c , (26) where c is the fractional occupancy of the Mn atoms by mobile Mn(IV) with a spindegeneracy factor β = 2. However, a β = 1 is to be expected because of the strong intraatomic exchange coupling between the mobile e electrons and the stationary t 3 conﬁguration. On lowering the temperature in the paramagnetic range, the mobile holes condense progressively into clusters and α(T ) increases as α(T ) = (k/e)(Eg/kT )

(27)

where Eg ≈ 0.02 eV is the enthalpy required to free a hole from a hole-rich second-phase cluster. However, α(T ) reaches a maximum value at a Tmax near the magnetic-ordering temperature in samples with 0.12 x 0.18; below Tmax , α(T ) decreases nearly linearly with decreasing temperature, reaching zero at a Tα as is illustrated for δ = 0.16 in ﬁg. 26. The matrix is a ferromagnetic insulator (FI) below Tα where α ≈ 0 μV/K. The opening of a small energy gap at the Fermi energy in a nearly ﬂat dispersion curve by charge and orbital ordering could give an α ≈ 0 μV/K and insulator behavior. This FI phase is to be compared to that found below a TOO < TC in the La1−x Srx MnO3 system over the range 0.10 < x < 0.17. In

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Fig. 26. Temperature variation of the resistivity ρ(T ) and thermoelectric power α(T ) for LaMnO3.16 , after Töpfer et al. (1996).

that system, an orbitally ﬂuctuating O* -orthorhombic ferromagnetic vibronic (FV) phase appears in the interval TOO < T < TC between the FI phase and a paramagnetic, polaronic O phase in the interval 0.10 < x 0.15; the FV phase transforms abruptly to a ferromagnetic metallic (FM) phase in the interval 0.15 < x 0.16, see ﬁg. 43. In the LaMnO3+δ system, the FM phase is stabilized in the interval 0.18 < δ < 0.20. Therefore, we can expect a FV conductive phase to appear in the interval Tα < T < TC of LaMnO3+δ , 0.10 < δ < 0.18. The remarkable ρ(T ) behavior found in the interval Tα < T < TC of ﬁg. 26 may be an artifact of the polycrystalline samples reﬂecting changes in grain-boundary resistance with temperature in the interval Tα < T < TC . Support for this conclusion comes from hydrostatic-pressure measurements of Markovich et al. (2000, 2001). Their initial experiments on La0.91Mn0.95O3 showed that the tolerance factor t increases with pressure; an unusually high compressibility of the mean Mn–O bond is characteristic of a double-well potential for the equilibrium bondlength. A subsequent study of ρ(T ) under pressure to 0.94 GPa was made on a La0.94Mn0.98O3 single crystal. At ambient pressure, the single-crystal ρ(T ) curve showed a smooth insulator-metal transition on heating at a TFI = 115 K and a metal–insulator transition at the Curie temperature TC = 210 K. A minimum resistivity of about 2.53 cm at TFI shows the sample is a “bad metal” in the interval TFI < T < TC typical of a FV percolating phase. Moreover, pressure stabilizes the FV phase relative to both the FI and paramagnetic polaronic phase; dTC /dP = 17 K/GPa and a dTFI /dP < 0 suppresses the FI phase by 0.94 GPa. The FI phase in La1−x Srx MnO3 is stabilized by pressure, which distinguishes the FI phase below TOO in that system from the FI phase below Tα in LaMnO3+δ where cation vacancies can be expected to trap out the holes they introduce. However, a simple trapping out of holes cannot account for the suppression of α(T ) and ferromagnetic order.

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Fig. 27. Variation with δ of magnetization per Mn atom at 5 K in a ﬁeld H = 40 kOe (30 kOe for δ = 0.18). Insert: Magnetization vs. applied ﬁeld H for δ = 0.05 and δ = 0.18 of LaMnO3−δ , after Töpfer and Goodenough (1997b).

Figure 27 shows the variation with δ of the magnetization M at 5 K in a ﬁeld H = 40 kOe. M (5 K, 40 kOe) approaches the spin-only ferromagnetic value only for 0.12 δ 0.14. As δ increases, another hole-rich antiferromagnetic phase appears within the FV matrix to give a dM/dT ≈ 0 at lower temperatures. The volume fraction of the antiferromagnetic clusters of the “cluster glass” increases with δ. A candidate for this hole-rich phase is the type-CE antiferromagnetic phase appearing at 50–50 Mn(III)–Mn(IV) in La0.5 Ca0.5 MnO3 (see sect. 3.6). However, in the rhombohedral phase appearing with δ 0.20, the antiferromagnetic phase cannot compete with the FM phase having itinerant e electrons. Allodi et al. (2001) found, by following the 139 La NMR signal of LaMnO3+δ samples as a function of temperature, an inhomogeneous wipeout of the NMR signal in a broad temperature interval for all the lightly doped samples; in LaMnO3.04 (TN = 125 K) it occurred over the range 75 K T 140 K. Comparison with muon-spin-rotation data ruled out the possibility that the wipeout is due to spin ﬂuctuations, which means it is due to electric-ﬁeld-gradient ﬂuctuations associated with orbital and/or bond-length ﬂuctuations. These data reveal fast nuclear relaxations in a volume fraction of vibronic charge transfer and “bad-metal” behavior. This wipeout phenomenon was not observed in either the parent compound LaMnO3 or in a hole-rich R-rhombohedral matrix; it is associated with phase segregation at the crossover from localized to vibronic behavior of the e electrons. At lower temperatures, the NMR signal was restored, indicating the charge carriers had become static in the time scale τ < 10−9 s as a result of orbital ordering in the FI phase. The Weiss constant θ of the Curie–Weiss paramagnetic susceptibility plot χ −1 (T ) reﬂects the mean magnitude of the interatomic exchange interactions. LaMnO3 has a θ > 0, which reveals that the ferromagnetic interactions in the (001) planes are stronger than the c-axis

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Fig. 28. Tentative phase diagram for LaMnO3+δ , 0 δ 0.18. Data from Töpfer and Goodenough (1997b). PI = paramagnetic insulator, CAFI = canted-spin antiferromagnetic (A-type) insulator, SGI = spin-glass insulator, FI = ferromagnetic insulator, MCS = metamagnetic canted-spin conﬁguration.

antiferromagnetic interaction; but a θ < TN signals that the ferromagnetic planes couple antiferromagnetically. As δ increases, the interval TN –θ decreases in the range 0 < δ 0.05. For the spin-glass ferromagnetic phases 0.08 δ 0.16, we ﬁnd θ > TC with θ –TC increasing dramatically with δ. In the paramagnetic phase, the strength and fraction of ferromagnetic interactions clearly increases with δ, and a large θ –TC signals the presence of considerable short-range ferromagnetic order above TC . Moreover, a slow rise of M(T ) on cooling through TC indicates the persistence of a paramagnetic volume below TC (Töpfer et al., 1996). It is clear that the compounds are magnetically inhomogeneous, which is another reﬂection of the segregation of orbitally disordered and orbitally ordered volumes. In the O -orthorhombic δ = 0.05 sample, the magnetization M(T ) taken on heating after cooling in zero applied ﬁeld showed a typical spin-glass behavior (Töpfer and Goodenough, 1997b) indicating the presence of ferromagnetic clusters with a TC > TN in the antiferromagnetic matrix. In this insulator, the ferromagnetic coupling would be due to vibronic superexchange in regions of orbital ﬂuctuations. These considerations lead us to propose the tentative phase diagram of ﬁg. 28. The orthorhombic-rhombohedral transition has been tracked by Wold and Arnott (1959). The two-phase region 0.05 < δ < 0.10 observed by room-temperature X-ray diffraction has been shown from the spin-glass behavior below Tf to extend over a wider compositional range be low 200√K, which indicates that a spinodal phase √ segregation separates the O -orthorhombic * (c/a < 2) from an O -orthorhombic (c/a ≈ 2) or R-rhombohedral phase. With neutron powder diffraction, Huang et al. (1997) have shown the two-phase region at 300 K in the inter-

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val 0.05 < δ 0.10 consists of an antiferromagnetic O phase and a ferromagnetic O* phase of smaller volume. At a higher value of δ, an R-rhombohedral phase transforms smoothly to a ferromagnetic monoclinic (P1121/a) phase that corresponds to the ferromagnetic cluster glass. At lower temperatures, the transition temperature separating the orbitally ﬂuctuating O* phase from the R phase extends to a higher value of δ than the transition between the O and R phases; percolation of the O* and not the O phase gives a ferromagnetic matrix that transforms to a ferromagnetic-insulator (FI) phase below TC in the interval 0.11 < δ < 0.14 whereas the spin-glass-insulator (SGI) phase is found for δ 0.11 where the percolating matrix is the O phase. The O* –R transition was not tracked below TC of the metamagnetic “cluster glass” (MCG) appearing in the interval 0.15 x 0.18. 3.4. (La1−y Ry )0.7A0.3 MnO3 : The CMR phenomenon The perovskite systems R1−x Ax MnO3 (A = alkaline-earth) have been studied both extensively and intensively because they exhibit an intrinsic “colossal negative magnetoresistance”, known as the CMR phenomenon, at and above a ferromagnetic Curie temperature TC on application of a high magnetic ﬁeld (Kusters et al., 1989; von Helmolt et al., 1993; Chahara et al., 1993). They also exhibit below TC an extrinsic giant magnetoresistance associated with tunneling of electron spins across grain boundaries; the MnO3 array has only majority-spin conduction electrons in the ferromagnetic state. Here we discuss the intrinsic CMR phenomenon. In the systems (La1−y Ry )0.7 A0.3 MnO3 , the ratio Mn(IV)/Mn = 0.3 is held constant and, by decreasing the tolerance factor t of eq. (1) by decreasing the mean ionic radius of the large A-site cations of the perovskite structure, the MnO3 array is changed from a ferromagnetic metal with itinerant σ ∗ electrons of e-orbital parentage in La0.7 Sr0.3 MnO3 to an antiferromagnetic insulator in Pr0.7Ca0.3 MnO3 , which has localized e electrons in ordered orbitals and charge ordering of the holes. In all these perovskites, the π -bonding t3 conﬁguration on the Mn atoms is localized with a spin S = 3/2, and dramatic changes in physical properties are found at the crossover from localized to itinerant behavior of the σ -bonding electrons of e orbital parentage. In accordance with the virial theorem of eq. (19), the crossover compositions exhibit a dynamic spinodal phase segregation by cooperative oxygen displacements on a small length scale into either hole-rich itinerant-electron and hole-poor localized-electron regions or into regions of e-orbital and charge disorder and those of e-orbital and charge order. The itinerant-electron and/or orbitally disordered regions are ferromagnetic and conductive; the orbitally ordered, localized-electron regions are poor electronic conductors, especially where they contain ordering of the mobile holes. The ferromagnetic, conductive phase may be stabilized relative to the antiferromagnetic localized-electron phase by various externally applied forces. The CMR phenomenon is illustrated in ﬁg. 29, which is taken from Hwang et al. (1995) for the system La0.7−x Prx Ca0.3 MnO3 (note: x = 0.7y of (La1−y Ry )0.7A0.3 MnO3 ). The Curie temperatures TC are marked by arrows. The magnetoresistance between 0 and 5 Tesla, deﬁned here as (ρ0T − ρ5T )/ρ5T , increases and TC decreases, both dramatically, as x increases in the range 0 x 0.6 even though the variation in tolerance factor is small. Moreover,

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Fig. 29. CMR at 5 T on cooling for different compositions 0 x 0.7 in the system La0.7−x Prx Ca0.3 MnO3 . Arrows indicate the Curie temperatures TC ; after Hwang et al. (1995).

the magnetic transition at TC is ﬁrst-order, but the resistance decreases smoothly with temperature on cooling through TC although exhibiting a thermal hysteresis. The x = 0.7 end member Pr0.7 Ca0.3 MnO3 exhibits an even more complex behavior (Roy et al., 2000; Jirák et al., 1985; Yoshizawa et al., 1995, 1996; Tomioka et al., 1995, 1996; Anane et al., 1999; Lees et al., 1996; Miyano et al., 1997; Fiebig et al., 1998, 1999; Ogawa et al., 1998; Cox et al., 1998; Moritomo et al., 1997a; Kiryukin et al., 1997; Asamitsu et al., 1997; Srivastava et

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al., 2000; Stankiewicz et al., 2000); it undergoes, on cooling, a charge-ordering transition at TCO ≈ 230 K followed by antiferromagnetic order below TN ≈ 150 K that develops at lower temperatures a canted-spin ferromagnetic component. The insulating antiferromagnetic state can be driven irreversibly to a ferromagnetic conductive state with a large release of heat not only by an applied magnetic ﬁeld, but also by the application of pressure, by the irradiation with visible light or X-rays, or by a high current. The complexity is characteristic of antiferromagnetic compositions having a tolerance factor t at the transition from antiferromagnetic to ferromagnetic behavior below their magnetic-ordering temperature. The resistive transition occurs where the localized-electron phase forms a percolating matrix within which the ferromagnetic regions are isolated in the absence of an external input. With the application of the external input, the ferromagnetic regions grow at the expense of the antiferromagnetic volume. The situation is analogous to that found in LaMn0.5Ga0.5 O3 , ﬁg. 13, except that here the ferromagnetic phase is mixed-valent and conductive. ↑↑ The tight-binding bandwidth Wσ = 2ztσ for the σ ∗ electrons of a single-phase MnO3 array with z = 6 like nearest neighbors is, from eqs. (7) and (8), Wσ ≈ 12εσ λ2σ cos φ cos(θij /2).

(28) (180◦ − φ)

The small changes in Wσ that result from increasing the bending φ of the Mn–O– Mn bonds on substitution of Pr3+ for La3+ cannot account for the dramatic change in TC , from 250 K for x = 0 to 80 K for x = 0.6, or for that in the magnitude of the CMR phenomenon shown in ﬁg. 29 even though the increase in cos φ is enhanced by a transition from a larger equilibrium (Mn–O)localized to a smaller (Mn–O)itinerant bond length, eq. (20). However, the bandwidth of eq. (21) W = Wσ exp(−λεsc /h¯ ωo )

with λ ∼ εs /Wσ

(29)

is applicable where a dynamic spinodal phase segregation occurs; εsc is the energy required to transfer a hole from the hole-rich ferromagnetic phase to the hole-poor matrix and ωo is the frequency of the cooperative oxygen vibrations that separate the two phases. With eq. (29), we can attribute the change in physical properties with tolerance factor t, or bending angle φ, to changes in ωo with φ as well as to changes in the mean equilibrium (Mn–O) bond length. Egami and Louca (1999, 2002) have emphasized that there are two vibrational modes of the oxygen atoms that might impact the Mn–O bond length where the (180◦ −φ) Mn–O–Mn bond is bent from 180◦ : one is the breathing mode in which an oxygen atom moves close to one Mn nearest neighbor and away from the other; the second is a vibration perpendicular to the bond in which the two neighboring Mn atoms are impacted equally. A breathing mode would occur at the interface between localized and itinerant phases; displacements perpendicular to a bond would occur within phases. Spinodal phase segregation and vibronic conduction occur where the time for a hole to travel from one Mn atom to another is τh ≈ h¯ /W ≈ ωo−1 , or W ≈ h¯ ωo . Small changes in ωo with bending angle φ can change a W < h¯ ωo where conduction is polaronic into a W > h¯ ωo where the electrons become itinerant. A de Gennes double exchange associated with itinerant σ ∗ electrons would give a much higher TC than a vibronic superexchange augmented by a Zener double exchange, and TC increases dramatically where the volume fraction of itinerant

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electrons increases just below TC . Moreover, the ﬁrst-order character of the transition at TC signals a discontinuous change in the volume fraction of the itinerant-electron phase, but the heterogeneous character of the material makes the resistivity change smoothly on cooling through TC . As the tolerance factor t decreases with increasing x, the volume fraction of the itinerant-electron phase above TC decreases and, therefore, the discontinuity in the volume fraction on cooling through TC increases. Therefore, the latent heat of the transition at TC increases with x in La0.7−x Prx Ca0.3 MnO3 . With decreasing temperature in the paramagnetic state, polaronic holes progressively condense out below a critical temperature into an itinerant-electron phase. The hole-rich regions have a higher Curie temperature TC∗ than the TC of the hole-poor matrix; the ferromagnetic spin–spin coupling of the matrix is progressively reduced as it becomes increasingly due to vibronic superexchange and the double-exchange component is reduced by trapping out of the mobile holes into the hole-rich clusters (Goodenough, 1997). The hole-rich clusters, on the other hand, may achieve a de Gennes double-exchange coupling that gives the higher TC∗ . As the bandwidth W decreases with increasing x, the double-exchange component of the coupling in the matrix decreases, so TC decreases. However, as TC decreases, more holes are trapped out in the hole-rich clusters in the paramagnetic phase, which feeds back to lower TC even more. Therefore TC decreases dramatically with increasing x, but not TC∗ . On application of a magnetic ﬁeld in the interval TC < T < TC∗ , the ferromagnetic phase is stabilized relative to the paramagnetic phase, and growth of the conductive ferromagnetic clusters to beyond percolation gives the CMR phenomenon. Although, the increase in the volume of the ferromagnetic phase in an applied magnetic ﬁeld dilutes its hole concentration, orbital disorder introduces ferromagnetic vibronic superexchange interactions. Nevertheless, the hole concentration must remain consistent with itinerant-electron or vibronic conduction in the hole-rich phase. As the temperature decreases, more holes are trapped out into the hole-rich conductive phase and the volume fraction of this phase can grow larger in an applied ﬁeld of 5 T, which decreases ρ5T at TC . Moreover, with fewer holes in the matrix, the resistivity ρ0T increases with decreasing temperature. Therefore, the magnetoresistance (ρ0T − ρ5T )/ρ5T at TC increases remarkably as TC decreases with increasing x. The growth of a conventional magnetic polaron in a magnetic ﬁeld also leads to a negative magnetoresistance having a maximum value at TC , and serious claims have been made (Nagaev, 1999, 2001a; Emin, 1998) that his model is applicable to the CMR phenomenon in the manganese oxides. In this model also, mobile charge carriers achieve a greater stability and mobility by congregating in regions of ferromagnetic order. The analogy is, therefore, quite complete without requiring the strong electron-lattice coupling implicit in a doublewell potential at the crossover from localized to itinerant electronic behavior; it relies instead on the electron-spin interactions alone. However, the sensitivity of TC to the tolerance factor and the data to be presented argue for a model in which the electron-spin interactions are supplemented by strong electron–phonon interactions due to a double-well potential at the crossover from localized to itinerant electronic behavior. On the other hand, phase segregation into hole-rich and hole-poor regions needs to be supplemented in the manganese-oxide perovskites by consideration of the Jahn–Teller site deformations that occur at localized-electron Mn(III) : t3 e1 conﬁgurations. It is the dynamic Jahn–Teller orbital ﬂuctuations that give rise

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to the ferromagnetic vibronic-superexchange interactions in the hole-poor matrix. Where the cooperative deformations become long-range statically ordered, anisotropic antiferromagnetic interactions are introduced as in LaMnO3. This type of order occurs within a percolating matrix where the tolerance factor is lower than a critical value tc . Moreover, an applied magnetic ﬁeld can stabilize an orbitally disordered ferromagnetic phase relative to an orbitally ordered antiferromagnetic phase as was seen to be the case in the single-valent compound LaMn0.5Ga0.5 O3 , ﬁg. 13. An antiferromagnetic to ferromagnetic transition can also be induced by a pressure that increases a t < tc to a t > tc or by a 16 O/18O isotope exchange that changes tc , as is shown below for the system (La1−y Ndy )0.7Ca0.3 MnO3 . In a mixed-valent system, stabilization of a ferromagnetic phase containing orbital and charge disorder relative to an antiferromagnetic phase having ordered orbitals and charge can also be accomplished by the application of an electric ﬁeld or by electromagnetic irradiation that disorders the charge and the occupied e orbitals. All these features are illustrated by Pr0.7 Ca0.3 MnO3 . The Nd3+ ion is smaller than Pr3+ , so the critical tolerance factor tc for (La1−y Ndy )0.7Ca0.3 MnO3 occurs at a y < 0.6 rather than at a y 0.9 as in (La1−y Pry )0.7Ca0.3 MnO3. Figure 30 shows (Archibald et al., 1996) the temperature dependence of the thermoelectric power α(T ) for several compositions in the range 0.2 y 0.75. At atmospheric pressure, the √ 0.55 < y 1 samples with 0.946 t 0.952 are in the O -orthorhombic (c/a < 2) phase and undergo a second-order polaronic-polaronic transition at a Néel temperature TN to a weakly canted antiferromagnetic spin conﬁguration as occurs in PrMnO3. However, a chargeordering temperature√was not noted. The 0 y 0.55 samples are in the pseudocubic O*-orthorhombic (c/a ≈ 2) phase and undergo a ﬁrst-order phase change at a ferromagnetic Curie temperature TC , from which we deduce a critical tolerance factor tc ≈ 0.955. The temperature dependence of the resistivity ρ(T ) exhibits a strong maximum at TC in the O* phase as in La0.7−x Prx Ca0.3 MnO3 with x 0.6, ﬁg. 29; ρ(T ) continues to increase with decreasing temperature below TN in the O phase, and it was not possible to obtain a stable measure of α(T ) below TN in this phase. The maximum in α(T ) occurs at a Tmax a little above TC in the O* phase. Five other features of ﬁg. 30 are noteworthy. First, α(T ) approaches a temperature-independent value of −20 μV/K in the O* samples at high temperatures; this value is somewhat larger in the O sample, ﬁg. 31. A temperatureindependent α is indicative of polaronic conduction in which the statistical term, eq. (26), dominates any transport contribution. In eq. (26), the spin-degeneracy factor is β = 1 because of the strong intraatomic exchange at the Mn atoms; c is the fraction of available sites that are occupied by charge carriers. For small polarons, c = xN/N = x would give a value α = +38 μV/K whereas a two-Mn Zener polaron would correspond to c = xN/(N/2) = 2x to give the observed α = −20 μV/K. Therefore, we conclude that at high temperatures there is a progressive transition with increasing tolerance factor from small polarons to two-Mn polarons as t increases, complete conversion occurring for t > 0.995. At still higher values of t, a transition from two-Mn polarons to itinerant electrons can be anticipated. Indeed, in La0.7 (Ca1−y Sry )0.3MnO3 the transition at TC changes from ﬁrst-order to second-order with increasing y, ﬁg. 32, and both TC and dTC /dy change discontinuously at the crossover of TC and the orthorhombic-rhombohedral transition temperature TOR , ﬁg. 33; the electrons become itinerant in the paramagnetic state of La0.7 Sr0.3MnO3 (Tomioka et al., 2001) and

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Fig. 30. Thermoelectric power α(T ) for several compositions 0.20 y 0.75 of the system (La1−y Ndy )0.7 Ca0.3 MnO3 ; after Archibald et al. (1996).

La2/3 Sr1/3 MnO3 (Mira et al., 1999, 2000) as well as in La0.65Ba0.35 MnO3 , which has the highest tolerance factor t (McIlroy et al., 1996). Conﬁrmation of two-Mn polarons was found in the La1−x Cax MnO3 system by Mössbauer spectroscopy for x = 0.20 (Chechersky et al., 1997, 1999a) and by Mn K-edge X-ray extended ﬁne structure (EXAFS) for x = 0.25 (Lanzara et al., 1998).

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Fig. 31. High-temperature thermoelectric power α(T ) for y = 0.75 (t = 0.952 < tc ) and y 0.55 (t 0.957 > tc ) of the system (La1−y Ndy )0.7 Ca0.3 MnO3 , after Goodenough (1999).

Second, the sharp increase in α(T ) as T decreases to Tmax reﬂects a progressive condensation of the mobile holes into a hole-rich phase; shortening of the equilibrium Mn–O bond length in the hole-rich clusters transforms the τh > ωo−1 of the polaronic matrix to a τh ωo−1 of the hole-rich conductive clusters. The volume of the hole-rich phase increases with the number of holes that are trapped in it. The hole-rich clusters become superparamagnetic below a TC∗ > TC . On cooling through TC , the Weiss molecular ﬁeld increases the volume fraction of the conductive phase to well beyond percolation, releasing the trapped holes and lowering α(T ). Independent evidence for superparamagnetic clusters in the interval TC < T < TC∗ appears in the inverse magnetic susceptibility χ −1 vs. temperature (Goodenough and Zhou, 1998) shown in ﬁg. 34. The huge difference θ − TC , where θ is the hightemperature Weiss constant, reveals an anomalously extensive range of short-range ferromagnetic order above TC . Further evidence for phase segregation above and below TC has been obtained with a variety of other techniques in addition to Mössbauer (Chechersky et al., 1997, 1999a) and it has been possible to describe the structure of the low-energy optical conductivity with a two-phase model (Quijada et al., 1998). Kim et al. (1998) came to a similar conclusion from their optical-conductivity data, and Y.G. Zhao et al. (1998) used pulsed laser excitation to reveal a fast transient associated with photoionization of the polaronic phase and a slow transient associated with the hole-rich clusters in La0.7Ca0.3 MnO3 . Sakaie et al. (1999) have conﬁrmed with 139La NMR a slow correlation time for the spin–spin ﬂuctuations

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Fig. 32. The resistivity vs. temperature for La0.7 (Ca1−y Sry )0.3 MnO3 crystals with varying y. The anomaly at ca. 370 K for y = 0.45 is due to the orthorhombicrhombohedral transition. Inset shows inverse susceptibility vs. T /TC , after Tomioka et al. (2001).

Fig. 33. Phase diagram for La0.7 (Ca1−y Sry )0.3 MnO3 , after Tomioka et al. (2001).

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Fig. 34. Inverse magnetic susceptibility vs. absolute temperature for several samples R0.7 Ca0.3 MnO3 compared with LaMnO3 and La0.7 Ba0.3 MnO3 , after Goodenough and Zhou (1998).

of the ferromagnetic clusters and reported an anomalous temperature and ﬁeld dependence of the spin-lattice relaxation. Lu et al. (1997) and Fäth et al. (1999) have used tunneling scanning spectroscopy on, respectively, x = 0.35 and x = 0.30 of La1−x Cax MnO3 ﬁlms deposited epitaxially on a single crystal SrTiO3 substrate to observe directly the coexistence of the ferromagnetic phase and a polaronic phase both above and below TC and how the spatial extent of the ferromagnetic phase increases to beyond a percolation threshold on decreasing the temperature through TC or on applying a magnetic ﬁeld above TC . The CMR phenomenon occurs where the conductive ferromagnetic phase reaches a percolation threshold in the paramagnetic phase (Goodenough and Zhou, 1997). De Teresa et al. (1997) with neutron scattering. Chun et al. (2000) have measured the Hall constant and Hall mobility of single-crystal La0.7 Ca0.3 MnO3 (TC = 216.2 K) to demonstrate a transition from a low-temperature, ferromagnetic phase to a high-temperature polaronic phase in the interval TC < T < 1.4TC where ferromagnetic, metallic clusters coexist with the polaronic paramagnetic phase. Chechersky et al. (2000) have used 57 Co Mössbauer spectroscopy to identify the coexistence of two distinguishable ferromagnetic phases below TC in a well-characterized, homogeneous ceramic sample of La0.7 Ca0.3 Mn(57Co)O3 (TC = 245 K); the volume fraction of the minority phase decreases with decreasing temperature, and they observed a single ferromagnetic phase at lowest temperatures. Neutron-scattering data are consistent with this ﬁnding (Adams et al., 2000). Heffner et al. (2000) have used muon spin relaxation and neutron spin-echo measurements in ferromagnetic La1−x Cax MnO3 with x = 0.33 (TC = 262 K)

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and x = 0.30 (TC = 250 K), respectively, to identify two phases below TC that are distinguished by very different spin dynamics. The metallic matrix displayed diffusive relaxation with a diffusion coefﬁcient correlating with that of Mn spin waves obtained (Lynn et al., 1996; Vasiliu-Doloc et al., 1997) from neutron-scattering studies of the metallic ferromagnetic phase. The second phase, which was conﬁned to spatially separated clusters 30 Å in diameter, possessed more slowly ﬂuctuating spins and a linewidth independent of the muon wave number q, which signals a more insulating phase. We identify the former with the holerich phase, the latter with the hole-poor phase. As the temperature decreased below TC , the matrix grew at the expense of the minority, slow-relaxation phase. X.J. Liu et al. (2001a) have observed photoinduced changes in transmission through La0.7Ca0.3 MnO3 (TC = 200 K) ﬁlms probed with a continuous wave (CW) Ar+ laser (Eprobe = 2.54 eV) and a CW Ti:Al2 O3 laser (Eprobe = 1.55 eV). The data showed a photoinduced creation of clusters at temperatures T < TC and a photoinduced annihilation of clusters at T > TC . X.J. Liu et al. (2001a) interpreted this ﬁnding to be the creation of charge-ordered clusters (T < TC ) or annihilation of metallic clusters (T > TC ) since the matrix changes from polaronic to itinerant/vibronic on cooling through TC . It is unlikely that electron excitations would create a charge-ordered phase. Therefore, we suggest that the light perturbs the periodic potential of the itinerantelectron phase by exciting electrons from narrow σ ∗ -band states to localized energy levels such as that of a Mn(II) ion, thereby favoring the polaronic over the itinerant-electron phase. This interpretation is supported by a similar experiment made on a La0.7 Sr0.3 MnO3 ﬁlm (TC = 350 K) at temperatures T < TC , which showed the creation of polaronic clusters from the itinerant-electron matrix (X.J. Liu et al., 2001b, 2001c). The third feature of ﬁg. 30 to be noted is the maximum in α(T ) found at a Tmax a little above TC ; it increases dramatically as the tolerance factor t is lowered to the O –O* phase boundary appearing in the interval 0.952 < t < 0.957 because the concentration of mobile holes in the matrix decreases with T . Comparison of ﬁg. 30 and ﬁg. 35 shows a pressure dependence dt/dP > 0, which is the anomalous case of eq. (3b), indicating the presence of a double-well potential for the equilibrium (Mn–O) bond length in accordance with eq. (20) for the crossover from localized to itinerant behavior of antibonding electrons. The large compressibility of the (Mn–O) bond length in the two-phase domain has been corroborated by several experiments. Radaelli et al. (1997a) have used high-resolution neutron diffraction to show for La0.75Ca0.25 MnO3 an anomalous decrease in the volume on cooling through TC where the fraction of the ferromagnetic itinerant-electron phase increases sharply. The decrease in mean cell volume occurred despite an increase in the (180◦ − φ) Mn–O–Mn bond angle because a signiﬁcant decrease in the (Mn–O) bond length overcompensated for the increase in bond angle. De Teresa et al. (1996a) measured the magnetoresistance (MR) and the magnetothermal expansion (ME) for La2/3 Ca1/3 MnO3 and found a strong correlation between the two in the paramagnetic phase just above TC . They concluded that the increase in the volume fraction of the conductive ferromagnetic phase responsible for the MR is also responsible for the large volume contraction. Neumeier et al. (1995) and Laukhin et al. (1997) have found a dTC /dP > 0 that increases as TC decreases; the effect disappears in the O phase where there is a TN . Fontcuberta et al. (1998) have also shown that isovalent substitutions in (La1−y Ry )2/3 (Ca1−x Srx )1/3 MnO3 yield a dTC /dP > 0 that increases with the extent of local

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Fig. 35. Pressure dependence of α(T ) for (La0.6 Nd0.4 )0.7 Ca0.3 MnO3 with t = 0.960 > tc ; after Archibald et al. (1996).

disorder at the A-site cations, but the variations with disorder were not enough to account for the large dTC /dP that was observed. De Teresa et al. (1996b) have provided a comprehensive investigation of La2/3 Ca1/3 MnO3 that links the large pressure dependence of TC directly to the coexistence of two distinguishable phases, a conductive ferromagnetic phase of smaller volume and a paramagnetic polaronic phase of larger volume. Fourth, Jaime and Salamon (1999) have pointed out that α(T ) increases more sharply than exponentially on cooling to Tmax in ﬁg. 30 and that the additional entropy transported increases on crossing the O –O* phase boundary at tc . This observation is consistent with a progressive transformation from Zener to small polarons in the hole-poor phase as the hole concentration x = 0.30 in this phase is diluted by the trapping of Zener polarons in the holerich phase. Such a transformation would double the number of sites available to a polaron and would therefore increase the α of eq. (26) by reducing c = (1 − r)2x toward c = (1 − r)x, where r is the ratio of trapped to free polarons. In the O phase, most of the polarons appear to be small polarons at TN . Fifth, ﬁg. 36 shows the temperature dependence of the resistivity ρ(T ) as a function of pressure for the y = 0.75 sample, which is just on the O side of the O –O* phase boundary (t < tc ) at atmospheric pressure, and ﬁg. 37 shows the change in α(T ) with pressure for the same sample (Zhou et al., 1996). A resistivity maximum occurs at TC where a long-

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Fig. 36. Pressure dependence of ρ(T ) for (La0.25 Nd0.75 )0.7 Ca0.3 MnO3 with t = 0.952 < tc ; after Zhou et al. (1996). Lower inset shows ρ(T ) at low temperatures; upper insets show TC and ρ(30 K), ρ(250 K) vs. pressure.

range Weiss molecular ﬁeld increases the volume fraction of the conductive ferromagnetic phase to beyond percolation. The drop in ρ(T ) on cooling through TC is continuous even though the thermal hysteresis in ρ(T ) shows that the magnetic transition is ﬁrst-order. It has been commonly assumed that the metallic temperature dependence of ρ(T ) below TC signals itinerant-electron behavior. However, ﬁg. 36 shows that ρ(T ) remains above the itinerant-

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Fig. 37. Pressure dependence of α(T ) for (La0.25 Nd0.75 )0.7 Ca0.3 MnO3 with t = 0.952 < tc ; after Zhou et al. (1996). Inset details low-temperature data.

electron limit, which makes the ferromagnetic phase below TC a “bad metal”. Moreover, the drop in α(T ) to a small, temperature-independent value, as shown in ﬁg. 37, is not characteristic of a conventional metal. Since eq. (26) is not applicable at low temperatures, we turn to the general expression for the thermoelectric power (MacDonald, 1962): α = α0 + δα,

(30)

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Fig. 38. Speciﬁc heat vs. temperature for several samples with t > tc for (La1−y Ndy )0.7 Ca0.3 MnO3 ; after Overend et al. (unpublished).

where δα is a low-temperature enhancement factor normally associated in a metal with a phonon drag having a maximum contribution at a temperature Tmax ≈ 0.2θD , θD is the Debye temperature, and (ε − εF ) σ (ε) k α0 (T ) = − (31) dε e kT σ in which σ (ε) = f (ε)[1 − f (ε)]N(ε)μ(ε) is the product of the Fermi distribution function f (ε), the energy density of one-particle states N(ε), and the particle mobility μ(ε) at an energy ε relative to the band edge. In a metallic conductor, α0 becomes Mott’s expression: π 2 k 2 T ∂ ln σ (ε) . α0 ≈ − (32) 3eεF ∂ ln ε ε=εF Below TC , the conductive ferromagnetic phase of ﬁg. 37 shows no phonon-drag enhancement (δα = 0) and does not vary linearly with T as predicted by eq. (32). It follows from eq. (31) that a temperature-independent α ≈ 0 μV/K below TC implies σ (ε − εF ) ≈ σ (εF − ε), which means that there is little dispersion in the electron energies ε(k) of the σ ∗ band of e-orbital parentage. Moreover, the speciﬁc-heat data of ﬁg. 38 (Overend et al., unpublished) show that the -point anomaly at TC vanishes on the approach to the O –O* phase boundary (y = 0.55 sample), which is typical of spin-glass behavior below TC where ferromagnetic clusters are in an antiferromagnetic matrix. At the phase boundary, the Mn(III) e orbitals of the holepoor matrix order as in the O phase in zero applied ﬁled, but become disordered in a modest applied ﬁeld as occurs in LaMn0.5Ga0.5O3 , ﬁg. 13. We conclude that the charge carriers are

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Fig. 39. The fraction η of Mn sites without local Jahn–Teller distortions at 10 K and the Curie temperature TC of various R0.7 A0.3 MnO3 compounds vs. the 9-coordinated ionic radii rA ; after Louca et al. (2001).

vibronic below TC with a probability of electron transfer from a Mn(III) to a Mn(IV) ion τh−1 ≈ ωo ; the charge carriers are strongly coupled to local oxygen-vibration modes that, if long-range ordered, could give rise to mobile stripes of alternating itinerant and localized states. Clariﬁcation of the character of the charge carriers in the ferromagnetic phase of the materials exhibiting a large CMR phenomenon remains a challenge. An important tool for investigating the ordering of cooperative bond-length ﬂuctuations at the crossover from localized to itinerant-electron behavior and/or those due to orbital ﬂuctuations is the pulsed-neutron atomic pair-density-function (PDF) method developed by Egami (2001). Louca et al. (2001) have employed this method to determine the nature of the transition from polaronic to itinerant-electron behavior with changes in the mean room-temperature ionic radius rA of the A-site ions for a series of R0.7 A0.3 MnO3 compositions. They found Jahn–Teller distortions and Mn(IV) small polarons at 10 K if rA is less than 1.17 Å and six equivalent (Mn–O) bonds at each Mn atom of itinerant-electron length if rA is greater than 1.24 Å. In the narrow range 1.17 Å< rA < 1.24 Å, the volume fraction η of the itinerantelectron phase increased continuously and the Curie temperature TC tracked η; ﬁg. 39. Moreover, analysis showed that the short (Mn(IV)–O) bond length corresponded to half the Mn–Mn separation in the (001) planes for an rA in the range 1.19 to 1.20 Å, indicating that an rA larger than 1.20 Å would increase the Mn–O–Mn bond angle to a value that approached and then exceeded the critical angle for crossover from localized to itinerant electronic behavior. A bent (180◦ − φ) bond angle allows adjustment of the Mn–O–Mn bond length in different domains without changing the Mn–Mn separation by displacements of the oxygen atoms perpendicular to the bond axis and oxygen displacements along a bond axis at a phase interface. Therefore, at the crossover angle, the ﬁrst-order character of the transition from localized to itinerant electronic behavior allows phase segregation by cooperative oxygen displacement perpendicular to the Mn–O–Mn bond axis that create shorter Mn–O bonds in the itinerantelectron phase and longer Mn–O bonds in the localized-electron phase. These cooperative oxygen displacements may ﬂuctuate to give phase ﬂuctuations. This analysis provides insight into the sensitivity of the bandwidth W of eq. (28) to the vibrational frequency ωo at the crossover from polaronic to itinerant-electron behavior; the perpendicular vibrations harden as the Mn–O–Mn bond angle bends from 180◦ . Billinge et al. (2000) have used the PDF technique to show a similar continuous evolution from polaronic to itinerant-electron behavior on

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traversing the insulator-metal transition whether with increasing rA , i.e., tolerance factor, or decreasing temperature across TC in the La1−x Cax MnO3 system; polaronic behavior sets in at 20 K where rA decreases below 1.15 Å. Rivadulla et al. (2001), using literature neutrondiffraction data, have shown that the polaronic, antiferromagnetic phase converts abruptly to the conductive, ferromagnetic phase where the Mn–O–Mn bond angle θ = (180 ◦ − φ) changes from 157◦ in Pr2/3 Ca1/3 MnO3 to θ = 159.5◦ in (La0.78Pr0.22 )2/3 Ca1/3 MnO3 . At this transition, the ratio Q3 /Q2 of the tetragonal/orthorhombic Jahn–Teller distortional modes

√

√ tan Φ = ± 2/ 6 (2m − l − s)/ 2/ 2 (l − s) (33) changes from Φ = 23◦ to Φ = 25◦ . In eq. (33) s and l are the short and long (Mn–O) bond lengths in the (001) planes and m is the intermediate-length (Mn–O) bond along the [001] axis. A Φ = 30 ◦ is the strong-anisotropy all-Q3 limit m = s whereas Φ = 0 corresponds to the Q2 limit where, in the perovskite structure, m = l = s and the six (Mn–O) bond lengths at a Mn atom are equivalent. For further evidence of strong electron coupling to oxygen vibrations in a system that has two electronic phases, we turn to studies of 18 O/16 O isotope exchange. Isotope exchange does not change the Mn–O–Mn bond angle (180◦ −φ), which would leave Wσ of eq. (27) −1/2 unchanged; but it does change ωo ∼ Mo , where Mo is the oxygen mass, and therefore W of eq. (28) and τh ≈ h¯ /W . G.-M. Zhao et al. (1996, 1997a, 1997b) were the ﬁrst to show a dramatic decrease of TC on the exchange of 18 O/16O. If on cooling through TC the transition was from a global polaronic phase with τh > ωo−1 to a global itinerant-electron phase with −1/2 τh ≈ h¯ /W < ωo−1 , then the exchange of 18 O/16 O, which decreases ωo ∼ Mo , should favor the itinerant-electron phase with τh < ωo−1 and therefore raise TC . The fact that 18 O/16 O exchange decreases TC is, therefore, evidence that TC depends on a bandwidth W described by eq. (28) as a result of the two-phase character of the electronic system; a decrease in W with increasing Mo favors the polaronic phase and lowers TC if the transition is governed by the bandwidth W rather than by Wσ . If the dramatic change in TC with tolerance factor t in ﬁg. 29 is due to a change in ωo (φ), as is suggested by a TC ∼ W and eq. (29), then the critical ambient tolerance factor tc for the O –O* transition should increase and TC decrease accordingly on the exchange of 18 O for 16 O whereas pressure should have the opposite effect. In order to probe this deduction, Zhou and Goodenough (1998) undertook additional isotope-exchange experiments. Figure 40 compares the α(T ) curves at atmospheric pressure for the 18 O and 16 O (La0.25Nd0.75)0.7Ca0.3 MnO3 samples (t < tc ) of ﬁgs. 36 and 37. Comparison of these two curves with ﬁg. 31 shows that the change in α(T ) on exchanging 18 O for 16 O is equivalent to reducing t. This experiment provides direct evidence that the sensitivity with respect to t of the magnetic and transport properties of ﬁg. 29 depends more on the sensitivity of t to ωo (φ) than to Wσ . Nagaev (2001b) has argued that the isotope effect is due to oxygen off-stoichiometry, but this position does not appear to be tenable. Chechersky et al. (1999b) have provided further conﬁrmation of our conclusion. They followed with Mössbauer spectroscopy the temperature dependence through TC of the two-phase character of La0.8 Ca0.2 MnO3 and found the strength of the exchange interactions at 78 K were not changed by 18 O/16 O exchange whereas a considerable softening

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Fig. 40. Comparison of α(T ) for 18 O and 16 O at atmospheric pressure for (La0.25 Nd0.75 )0.7 Ca0.3 MnO3 samples of ﬁgs. 36 and 37; after Zhou and Goodenough (1998).

of the anharmonic Mn–18O–Mn vibrations reduced the volume fraction of the ferromagnetic phase at a given temperature. To obtain information on the variation of TC with pressure for 18 O vs. 16 O, Zhou and Goodenough (1998) used the fact that ρ(T ) for (La0.25Nd0.75)0.7 Ca0.3 MnO3 in ﬁg. 36 has its maximum value near TC . Three additional features of ﬁg. 36 are noteworthy: 1. The ρ(T ) curves are relatively insensitive to pressure for T > TC , but they change dramatically for T < TC on crossing a transition at Pc < 4 kbar. The transition, not shown in ﬁg. 36, is sharply deﬁned. 2. There is no thermal hysteresis in the ρ(T ) curve at atmospheric pressure where (La0.25Nd0.75)0.7Ca0.3 MnO3 is in the O phase at the magnetic-ordering temperature, but a pronounced thermal hysteresis appears at pressures P > Pc . 3. The thermal hysteresis, which marks a change from a second-order transition at TN to a ﬁrst-order transition at TC on crossing the O –O* phase boundary, decreases as TC increases with pressure P > Pc . Figure 41 (top) compares the evolution with pressure of TC and thermal hysteresis at TC of the (La0.25Nd0.75)0.7Ca0.3 MnO3 sample with 16 O and 18 O. A shift of ΔPc ≈ 9 kbar on isotope exchange reﬂects the increase in effective tc , and a giant isotope coefﬁcient d ln TC /d ln Mo ≈ 4.9 appears abruptly on conversion from the O to the O* phase; no measurable isotope shift was found in the antiferromagnetic O phase containing small-polaron holes. Ordering of the occupied e-electron orbitals into the (001) planes in the O phase is stabilized by a softer −1/2 ωo ∼ Mo , which shows it is not the bending angle θ = (180◦ –φ) of the Mn–O–Mn bond per se that controls the O –O* transition; it is the dependence of ωo , and hence of W of eq. (28), on φ that makes the polaronic to itinerant-electron transition vary so sensitively with θ . The large isotope shift of TC is clearly associated with an instability of the static Jahn– Teller orbital ordering on the approach to a transition from localized to itinerant electronic

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Fig. 41. Variation of TC with increasing and decreasing pressure for 16 O and 18 O for three samples of (La1−y Ndy )0.7 Ca0.3 MnO3 , of ﬁgs. 36 and 37: y = 0.75 (#1, top) and y = 0.8 and 0.85 (#2 and #3, respectively, bottom); after Zhou and Goodenough (1998) .

behavior where the (Mn–O) bond length has a double-well potential. It is at such a transition that we ﬁnd the coexistence of two phases, one hole-rich with itinerant electrons and the other hole-poor with cooperative Jahn–Teller distortions that may be static or ﬂuctuating. The magnitude of ΔTC in the O* phase on 18 O/16 O exchange increases with the magnitude of dTC /dt > 0, which is a maximum just above tc . The isotope shifts of TC in samples with t > tc at ambient pressure were similar to those reported by G.-M. Zhao et al. (1996, 1997a, 1997b). Franck et al. (1999, 2001) have reported an analogous ﬁnding in La1−x Cax MnO3 for 0.2 < x < 0.3 and an increase of ΔTC in the oxygen-excess x = 0.2 compound that does not support the Nagaev (2001b) calculation, but is due to the perturbation of the periodic potential of the MnO3 array as a result of the cation vacancies present. In the O phase, TN is determined only by superexchange interatomic interactions; the small-polaron hopping rate is too slow relative to a spin-relaxation time for a double-exchange coupling to be operative. However, the charge carriers are more mobile in the O* phase and they contribute a double-exchange component to the vibronic ferromagnetic superexchange interactions of the matrix that increases with the volume fraction of the conductive ferro-

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magnetic phase. The dTC /dt > 0 reﬂects an increase with tolerance factor t in the doubleexchange contribution to the magnetic interactions as the (180◦ − φ) Mn–O–Mn bond angle −1/2 increases. The larger mass Mo of an 18 O softens ωo ∼ Mo , which lowers ω(φ) for a given value of φ; the volume fraction of the conductive ferromagnetic phase decreases as ωo softens and the effective tc increases. Above the temperature of condensation of the itinerant-electron phase, the small polarons break down ﬁrst by forming two-Mn Zener polarons and then, as W increases further, become itinerant holes. On cooling, the Zener polarons may order or may condense into a 1D or 2D itinerant-electron σ ∗ band where a 3D σ ∗ band would be narrow enough for orbital ordering. The reduction of W on 18 O substitution for 16 O increases the small-polaron/Zener-polaron ratio as is made evident by the increase in the high-temperature magnitude of α(T ) in ﬁg. 40. In order to identify any dependence on Mo of the character of the charge carriers in the majority conductive phase below TC , we minimized any pressure dependence by examining a 16 O sample of lower t having a Pc close to that of the 18 O-substituted (La0.25Nd0.75)0.7Ca0.3 MnO3 sample. For this purpose, Zhou and Goodenough (1998) measured the pressure dependence of ρ(T ) for two additional 16 O samples, 2 and 3 with (La0.2 Nd0.8) and (La0.15Nd0.85) corresponding, respectively, to t = 0.951 and 0.949. Figure 41 (bottom) shows that the 16 O sample 3 has nearly the same Pc ≈ 11 kbar as the 18 O sample having a t = 0.952. It follows that the exchange of 18 O for 16 O is equivalent to a shift of tolerance factor Δt ≈ −0.03; hydrostatic pressure is equivalent to an increase of t by dt/dP ≈ 2.7 × 10−3 per kbar. From ﬁg. 41, they also observed at Pc = 11 kbar for 16 O (La0.15Nd0.85) and 18 O (La0.25Nd0.75), respectively, a thermal hysteresis ΔTC = 27 K and 19 K; on cooling, a dTC /dP = 4.0 K/kbar and 2.7 K/kbar. The thermal hysteresis ΔTC should be proportional to the volume change ΔV at the ﬁrst-order transition, which in turn would be proportional to the change in the mean electronic potential energy ΔV . From the virial theorem, eq. (19), it follows that ΔTC ∼ ΔT |TC

(34)

is a measure of the change ΔT in the mean kinetic energy of the charge carriers at the ﬁrstorder transition at TC . At temperatures T > TC , the charge carriers are polaronic and the ratio of small to Zener polarons is larger for the 18 O sample at Pc . Since itinerant electrons would have a mean kinetic energy essentially independent of Mo , a ΔTC (18 O) > ΔTC (16 O) would follow from eq. (34), which is just the opposite to what is observed. Therefore, these data also lead to the conclusion that in the O* phase near the O –O* phase boundary, the charge carriers below TC are not conventional itinerant electrons, but interact strongly with the lattice to form “vibronic” states with a bandwidth described by eq. (29) rather than eq. (28). We also note that a larger dTC /dP of the 16 O vs. 18 O sample is consistent with a smaller trapping energy of the polarons in the paramagnetic state of the 16 O sample evident in ﬁg. 40. G.-M. Zhao et al. (2001) have subsequently shown an isotope shift of the intrinsic resistivity of the conductive ferromagnetic state of high-quality epitaxial ﬁlms of two CMR manganites, La0.75 Ca0.25MnO3 and Nd0.7Sr0.3 MnO3 , that supports a polaronic charge-carrier effective mass m∗ = m exp(λεx /h¯ ωo ) below TC as also follows from the vibronic bandwidth W of eq. (29). Alexandrov et al. (2001) have developed a theory of a “polaronic Fermi liquid” in which m∗ = m exp(A/ωo ); their model corresponds to the “vibronic” state.

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Fig. 42. Magnetic phase diagrams of (La0.25 Pr0.75 )0.7 Ca0.3 Mn18 O3 after (a) ZFC and (b) FC procedures; open circles from M(T ) and closed circles from NMR. PS = phase separation, after Yakubovskii et al. (2000).

Babushkina et al. (2000) examined the effect of partial 18 O/16 O exchange on the x = 0.525 sample of La0.7−x Prx Ca0.3 MnO3 , see ﬁg. 29. On cooling, they found the ﬁrst-order transition at TC , and TC decreased linearly with 18 O content from 95 K for all 16 O to 50 K for 39% 18 O; the residual resistivity increased. The ρ(T ) curves changed with increasing 18 O content like those of ﬁg. 36 with decreasing pressure. Above 40% 18 O, the conductive ferromagnetic phase failed to percolate and remained as isolated clusters within an antiferromagnetic matrix, showing that the effective tolerance factor became t = tc at about 40% 18 O. Above 90% 18 O, the antiferromagnetic transition at T became second-order. Yakubovskii et al. (2000) N performed magnetization and NMR studies on the 18 O sample of La0.7−x Prx Ca0.3 MnO3 , x = 0.525. They showed that with increasing magnetic ﬁeld, the conductive ferromagnetic phase grows irreversibly to beyond percolation. As shown in ﬁg. 42, the zero-ﬁeld-cooled (ZFC) 18 O sample exhibits a magnetic-ﬁeld range in which the ferromagnetic volume fraction grew to beyond percolation whereas a sample ﬁeld-cooled (FC) in H = 7 T has the ferromagnetic phase-separation (PS) region intersecting the temperature axis. An intrinsic capacitance associated with the charge-ordered phase below TCO = 225 K in Pr0.67 Ca0.33MnO3 was noted in the ac-impedance data by Rivadulla et al. (1999a); a drop in the paramagnetic susceptibility on cooling through TCO would be consistent with a preferred crystallographic orientation of two-Mn Zener polarons below TCO . Saraf et al. (2000) subsequently showed that strong dielectric anomalies also appear at TN ≈ 133 K, at the onset of spin

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canting near 116 K, and at an unidentiﬁed transition at about 125 K. These anomalies appear to reﬂect slow reorganization responses of a cooperative lattice deformation and/or charge distribution in an electric ﬁeld in the neighborhood of a transition where reorganization is occurring. Freitas et al. (2001) have studied the dynamic properties of the magnetization of La0.7−x Yx Ca0.3 MnO3 , 0 x 0.15, below a ﬁrst-order metal-polaronic transition at TC . As yttrium is added, there is a progressive appearance of cluster-glass behavior with a freezing temperature Tf < TC . This behavior is characteristic of the coexistence of a ferromagnetic and an antiferromagnetic phase below Tf . Savosta and Novák (2001) have shown the coexistence of two different ferromagnetic phases below TC in several R0.7 A0.3 MnO3 compositions, including La0.7 Ca0.3 MnO3 . Both phases are conducting, but one contains fast charge carriers and the other slower charge carriers. We would interpret the former to be itinerant charge carriers that give a de Gennes double-exchange ferromagnetism and the latter to be polaronic charge carriers of a vibronic (polaron Fermi liquid) phase containing a large component of vibronic-superexchange ferromagnetism. The characteristic dimension of the vibronic phase was a few nm in La0.7 Ca0.3 MnO3 , and its volume fraction decreased with decreasing temperature. Moreover, the volume fraction of this phase at a given temperature decreased with increasing Mn–O–Mn bond angle θ = (180◦ − φ) for a ﬁxed hole concentration. These data are consistent with the following interpretation of the system La0.7−x Yx Ca0.3 MnO3 in which θ decreases with increasing x. The volume fraction of the vibronic ferromagnetic phase below TC grows with increasing x. Ordering of the Mn(III) e orbitals below Tf transforms the vibronic ferromagnetic phase to a type-A antiferromagnetic polaronic phase. Isolated antiferromagnetic clusters create a cluster glass; they reduce the spontaneous magnetization of the sample and introduce a frustration of the magnetic interactions that increases progressively with the volume fraction of the antiferromagnetic phase. A high magnetic ﬁeld may disorder the Mn(III) e orbitals so as to convert the antiferromagnetic phase back to a ferromagnetic phase. Consistent with this interpretation is a study of the La2/3 (Ca1−x Srx )1/3 MnO3 system by Mira et al. (2002) that, together with literature data for (La1−y Ry )0.7 A0.3 MnO3 compounds, indicates a second critical tolerance factor tc∗ ≈ 0.98 (based on 12-fold rather than 9-fold coordination of A sites) for the O* -orthorhombic to R-rhombohedral transition, a ﬁrst-order magnetic transition occurring at TC in the O* phase (t < 0.98) and a second-order magnetic transition occurring at TC in the R phase (t > 0.98). This critical tolerance factor is to be contrasted with the tc = 0.955 for the change from the second-order magnetic transition at TN to the ﬁrst-order transition at TC that was investigated by pressure and by 18 O/16 O isotope exchange, ﬁg. 41. The large CMR phenomenon as well as a ﬁrst-order magnetic transition occurs in the range tc < t < tc∗ where TC increases dramatically with t; a discontinuous increase in the volume fraction of the more conductive ferromagnetic phase at TC makes the magnetic transition ﬁrst-order in accordance with the virial theorem, eq. (19). In summary, the magnetic and transport properties of the (La1−y Ry )0.7Ca0.3 MnO3 perovskites near the O –O* phase boundary are extraordinarily sensitive to the tolerance factor t, the oxygen mass Mo , temperature, and pressure as well as to magnetic and electric ﬁelds. This sensitivity can be attributed to strong electron-lattice coupling associated with not only order–

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disorder transitions of cooperative Jahn–Teller deformations, but also with an accompanying crossover from localized to itinerant electronic behavior of σ -bonding e electrons in the presence of localized t 3 conﬁgurations on the Mn atoms. At crossover, a hole-rich, conductive ferromagnetic phase segregates from a hole-poor polaronic phase that is antiferromagnetic where the cooperative Jahn–Teller distortions are long-range ordered, but is ferromagnetic where the distortions ﬂuctuate. Condensation of two-Mn Zener polarons into a hole-rich, conductive ferromagnetic phase with a TC∗ higher than the TC or TN of its matrix and growth of the hole-rich phase to beyond its percolation threshold in an applied magnetic ﬁeld in the interval TC < T < TC∗ results in the CMR phenomenon. A discontinuous increase in the volume fraction of the hole-rich phase on cooling through TC contracts the volume discontinuously and makes the magnetic transition ﬁrst-order; retention of two ﬂuctuating ferromagnetic phases below TC suppresses the phonons and makes the conductivity vibronic rather than itinerant. Orbital ordering in the hole-poor minority phase may occur at low temperatures to introduce magnetic frustration and cluster-glass behavior. The O –O* phase boundary depends upon the oxygen-vibration frequency; ωo > τh−1 gives polaronic conduction and ωo < τh−1 gives itinerant-electron behavior. The O –O* boundary and phase segregation occur where ωo ≈ τh−1 . The oxygen vibrations of interest have two components, perpendicular and parallel to a Mn–O–Mn bond axis, that harden as the bond angle θ = (180◦ − φ) decreases, and an ωo (φ) enters the vibronic bandwidth W of eq. (29) for the two-phase region. Moreover, the transitions occur where W ≈ h¯ ωo , which means that the phenomena vary sensitively with the tolerance factor t. The CMR phenomenon and a ﬁrst-order magnetic transition are found for 30% holes in the MnO3 array in the interval 0.955 < t < 0.98 where TC increases dramatically with t; this critical range of tolerance factors does not change signiﬁcantly in systems with varying hole concentration. 3.5. The system La1−x Srx MnO3 The phase diagram of La1−x Srx MnO3 , ﬁg. 43, has been constructed from data taken from several different sources (Urushibara et al., 1995; Kawano et al., 1996; Zhou et al., 1997, 2001b; Moritomo et al., 1997b; Dabrowski et al., 1999a; Xiong et al., 1999; Zhou and Goodenough, 2000; G.-L. Liu et al., 2001). Measurements of the temperature dependence of the transport properties and magnetic susceptibility under hydrostatic pressure have proved particularly helpful in determining, without changing composition, the nature of the transitions between competing phases that have been found in the range 0.10 x 0.20. In the range 0 < x < 0.1, the canted-spin antiferromagnetic phase is a small-polaron conductor, which classiﬁes it as an insulator (CAFI). Below TN , the antiferromagnetic component of the type-A magnetic order, eq. (14) and table 1, is oriented along the b-axis, the weak ferromagnetic component along the c-axis, and the Dzialoshinskii vector Dij is along the a-axis in space group Pbnm. A 139La study by Kumagai et al. (1999) has revealed the presence below TN of ferromagnetic droplets appearing as a second phase by x = 0.05. Hennion et al. (2000) have observed with elastic and inelastic neutron scattering from an untwinned x = 0.06 single crystal the presence of ferromagnetic droplets three (001) layers thick with an in-plane diameter of about 17 Å; the droplets are separated by distances 38 Å within the (001) planes.

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Fig. 43. Phase diagram for La1−x Srx MnO3 , 0 x 0.20, after Zhou and Goodenough (2001a).

These hole-rich droplets represent a ferromagnetic second phase having a TC < TN ; the volume fraction of this minority phase grows with increasing x, and in the range 0.1 x 0.13 the droplets are condensed into large clusters having TC > TN . The crossover from TC < TN to TC > TN occurs at about x = 0.10 near a point where the 2D orbital order–disorder transition (or onset of orbitally disordered clusters) at T ∗ (same T ∗ as in ﬁg. 14) crosses TN . The compositional dependence of the structural O –O* transition at TJT and the O* –R transition at TOR can be clearly followed by monitoring the temperature dependence of the resistance (Mandal et al., 2001); monitoring the variation with x of the higher-order transition at T ∗ from the resistance curve R(T ) is more subtle and has been accomplished with further aid from the thermoelectric power α(T ) measured on single crystals (Zhou and Goodenough, 2000). The transition from polaronic to itinerant electronic behavior in the paramagnetic Rrhombohedral phase has not been studied. In the narrow compositional range 0.10 x 0.13, a spin-glass behavior is found in very low applied magnetic ﬁelds below a spin-freezing temperature Tf . The spin-glass character of the magnetic ordering is manifested in the magnetic susceptibility (Skumryev et al., 2000) as well as in the collapse of the anomaly in the speciﬁc heat of the x = 0.10 sample at the magnetic-ordering temperature, ﬁg. 44. However, the spin glass is converted to a ferromagnetic phase in a modest applied magnetic ﬁeld with TC ≈ Tf ; the volume fraction of the ferromagnetic phase grows at the expense of the O antiferromagnetic phase in an applied magnetic ﬁeld, and the sample becomes “ferromagnetic” where the volume fraction of the ferromagnetic phase exceeds the percolation threshold. It is only below a TOO that the samples become fully ferromagnetic. The transition at TOO is ﬁrst-order, see the Cp data for x = 0.11 and x = 0.12, where there is a discontinuous change in the ferromagnetic volume fraction on

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Fig. 44. Magnetization M(T ) in H = 20 Oe and 5 kOe; speciﬁc heat Cp (T ) for La1−x Srx MnO3 , 0 x 0.19: O = Cp ; Δ = M(T ) in 5 kOe; simple solid line = M(T ) in 20 Oe. Arrows indicate warming vs. cooling curves, after G.-L. Liu et al. (2001).

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Fig. 44. Continued.

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cooling through TOO . For x 0.13, the system becomes ferromagnetic below TC in zero applied magnetic ﬁeld, and the transition at TOO becomes second-order. In ﬁg. 43, the FI phase appearing below TOO is labeled O -orthorhombic. The ferromagnetic-insulator (FI) phase appearing below TOO is both charge and orbitally ordered. Klingeler et al. (2002) who have also tracked the changes in the speciﬁc-heat anomalies appearing in the range TOO T TC , pointed out that the entropy changes can be accounted for with only the calculated changes in spin entropy and concluded that the phase changes must be driven by the exchange interactions. Therefore, the character of the orbital and charge order below TOO and how it supports 3D ferromagnetic interatomic interactions is an important question that remains controversial. Whether the ﬁrst-order transition at TOO in x = 0.125 is due to charge ordering as originally reported by Yamada et al. (1996) or to an orbitally ordered state as proposed by Endoh et al. (1999) appears to have been resolved by Yamada et al. (2000), who provided evidence for both orbital and charge ordering, but with the charge ordering appearing as a c-axis charge-density wave √ (CDW)√of opposite phase on neighboring c-axis Mn–O–Mn columns to give a unit-cell size ( 2 × 2 × 4)cubic. Ordering of long and short Mn–O bonds in the (001) planes as in LaMnO3 gives the ferromagnetic planar interactions of the type-A antiferromagnetic structure. Ordering of the holes into static CDWs along the c-axis rows can give ferromagnetic coupling along the c-axis as well. In the interval 0.05 x 0.10, the ferromagnetic plate-like second phase consists of hole-rich regions in which ferromagnetic coupling between ferromagnetic planes replaces the antiferromagnetic coupling of the type-A antiferromagnetic matrix. Transitions between the competing phases existing at x = 1/8 have been tracked by highfrequency conductivity measurements (F. Mayr et al., 2000) and exposure to X-rays has been shown (Casa et al., 2001) to induce conductive transitions with memory at temperatures T < TOO . In the range 0.13 x 0.15, TC and TOO increase with x; TC undergoes a ﬁrst-order jump where it crosses TJT . In the paramagnetic range TC < T < TJT , the O structure signals an ordering of the occupied e orbitals of the matrix into the (001) planes, but either the in-plane order ﬂuctuates or there are orbitally disordered clusters within the matrix (T > T ∗ ). Threedimensional orbital ﬂuctuations dominate in the interval TOO < T < TC where the system is a ferromagnetic vibronic conductor (FV). The greater orbital disorder is stabilized by ferromagnetic vibronic superexchange that supplements the Zener double exchange. The resistivity data of ﬁg. 45(a) reﬂect the transitions TJT , TC , TOO , and TOR . On cooling, the step increase at TJT shows the transition changes from second-order for x = 0.12 and 0.13 to ﬁrst-order at x = 0.14 where it approaches TC . This change is also evident in the speciﬁc-heat anomaly of ﬁg. 44. Rozenberg et al. (1994) have predicted that such a change should occur at a transition from localized to itinerant electronic behavior. The resistivity drops on cooling through TC as a result of reduction of the spin-disorder scattering; it increases abruptly on cooling through the ﬁrst-order transition at TOO in the x = 0.11 and 0.12 samples. By x = 0.14, the transition at TOO is no longer ﬁrst-order and is only marked by a smooth minimum in ρ(T ). For x > 0.15, the minimum in ρ(T ) at TOO is less sharp and drops sharply with increasing x. Moreover, the metallic conductivity in the interval TOO < T < TC changes abruptly from vibronic to itinerant; a pressure experiment on a single-

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Fig. 45. (a) Resistivity vs. temperature for melt-grown single-crystal samples of La1−x Srx MnO3 . Critical points; = TJT where |dρ/dT | is a maximum; Δ ≈ Tf or TC where dρ/dT is a maximum; O = TOO where ρ(T ) is a local minimum. TOR = midpoint of thermal hysteresis below TC for 0.17 x 0.19. Arrows indicate heating and cooling at thermal hysteresis loops, after G.-L. Liu et al. (2001).

crystal x = 0.14 sample (Zhou and Goodenough, 2000) showed the transition from vibronic to itinerant electronic behavior is ﬁrst-order, which conforms to prediction from the virial theorem of eq. (19), see ﬁg. 45(b). Although the FI phase below TOO changes character on crossing the vibronic-itinerant electronic transition in the O* phase, becoming more conductive in the range 0.15 < x < 0.17 where the temperature of the transition from FI to ferromagnetic metal (FM) decreases with increasing x, nevertheless a spinodal segregation into FI and FM phases at this ﬁrst-order transition was only detected in pressure measurements made on a single-crystal x = 0.16 sample (Zhou et al., 2001b). In the interval 0.13 x 0.15, the FV to FI transition occurs over an extended temperature interval where the magnetic-exchange driving force for orbital order is sharply reduced at a ferromagnetic-ferromagnetic transition.

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Fig. 45. (b) Pressure-temperature phase diagram below room temperature for La0.86 Sr0.14 MnO3 , after Zhou and Goodenough (2000).

The CMR phenomenon, not indicated in ﬁg. 43, occurs above TC in the O phase; it is largest at x ≈ 0.12 where isolated FV O* clusters in a paramagnetic O matrix grow to beyond percolation in an applied magnetic ﬁeld. This evolution with x of physical properties bears a striking resemblance to that which occurs with δ in the LaMnO3+δ samples. Uhlenbruch et al. (1999) and Nojiri et al. (1999) have shown that the FI phase below TOO is stabilized relative to the FV phase by an applied magnetic ﬁeld as can be expected for an exchange-driven transition. Senis et al. (1998) and Martínez et al. (2000) report that the FI phase is also stabilized by pressure whereas the FI phase in the LaMnO3+δ system was suppressed by pressure. This observation signals that the charges are more localized in the FI phase of LaMnO3+δ . The data of ﬁg. 43 reveal three distinguishable ferromagnetic phases: FV, FI, and FM. The ferromagnetic interactions in the FV phase are composed of vibronic superexchange supplemented by Zener double exchange; the interactions in the FM phase may be classiﬁed as de Gennes double exchange. Those in the (001) planes of the FI phase appear to be conventional superexchange interactions whereas those along the c-axis CDWs are unconventional.

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Fig. 46. Magnetization at 5 K in 50 kOe for La1−x Srx MnO3 , 0 x 0.35. Solid line: (4 − x)μB /Mn. Dashed line is a guide to the eye. Inset: M (5 K) vs. applied magnetic ﬁeld, after G.-L. Liu et al. (2001).

Figure 46 shows the evolution with x of the magnetization at 5 K in 50 kOe. The abrupt change from canted-spin to frustrated ferromagnet at x = 0.10 is dramatic. Signiﬁcant also is the observation that the saturation magnetization M (5 K, 50 kOe) has the spin-only theoretical value MS = (4 − x)μB /Mn for the FM phase x 0.18, but it is larger in the O phase in the range 0.11 < x < 0.18, reaching a maximum value of 4.4μB /Mn at x = 0.15. This enhancement of the saturation magnetization is unique to the O phase of the La1−x Srx MnO3 system; it has not been observed in the La1−x Cax MnO3 system where the insulator O phase does not occur. Although the orbital angular momentum is quenched in lowest-order perturbation theory at both Mn(III) and Mn(IV) in octahedral sites, the data indicate that where the Mn(III) e electrons are localized, an orbital contribution to the atomic moment is introduced by higher-order terms; where the electrons of e-orbital parentage are itinerant, the orbital contribution is suppressed. The orbital contribution is progressively suppressed as the mean hole mobility in the O phase increases with x in the range 0.15 < x < 0.18. Neutron-scattering experiments by Vasiliu-Doloc et al. (1998a) on an x = 0.15 sample showed the ferromagnetic order below TC = 235 K developed a canted-spin structure below

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Fig. 47. Temperature dependence of the thermal conductivity κ(T ) for selected single-crystal compositions of the system La1−x Srx MnO3 . (a) x = 0, 0.08 and LaMnO3+δ (δ = 0 and 0.07); the lines in κ −1 vs. T for x = 0 are linear ﬁtting.

a TCA = 205 K. Pressure experiments on an x = 0.14 single crystal showed a ﬁrst-order jump in TC where TJT crosses TC at about 2 kbar (Zhou and Goodenough, 2000) see ﬁg. 45(b); at ambient pressure the two ferromagnetic phases would have TC ≈ 205 K and 235 K on either side of the transition at TJT . Therefore, the change at 205 K may be attributed to crossing TJT in a phase a little more hole rich than x = 0.14. The long-wavelength magnetic excitations were conventional spin waves, but an anomalously strong quasielastic component developed at small wave vector above about 200 K where the two magnetic phases coexist. Asamitsu et al. (1995, 1996) have shown that an x = 0.170 sample can be switched from the O* -orthorhombic to the R-rhombohedral structure by the application of an external magnetic ﬁeld; the switching is reversible or irreversible depending on the temperature. Campbell et al. (1997) have conﬁrmed the phenomenon on a single-crystal x = 0.165 sample with neutron diffraction. The x = 0.17 composition sits in the FI-FM two-phase region. The temperature dependence of the thermal conductivity for selected single-crystal compositions over the range 0 x 0.12 are shown in ﬁg. 47 (Zhou and Goodenough, 2001a, 2001b). They were chosen to probe the changes occurring on crossing the several phase transitions shown in ﬁg. 43. Whereas the x = 0 compound exhibits a strong phonon component, κ(T ) is strongly suppressed at all temperatures in the x = 0.08 samples where holes, partic-

320 J.B. GOODENOUGH Fig. 47. (b) x = 0.12, 0.14, 0.15, 0.16, 0.17, 0.19: open circles for κ(T ), dashed line is κ–κ e where the electronic component κ e was obtained from the Wiedermann–Franz Law, solid line is for resistivity ρ(T ), after Zhou and Goodenough (2001a).

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ularly mobile holes, introduce orbital ﬂuctuations that eliminate the phonon contribution. In the x = 0.12 sample, κ(T ) is extremely small in the O* phase above TOO ; there is only a small increase in κ(T ) on cooling through TJT where the orbital disorder changes from 3D to 2D on entering the O phase above T ∗ and there is a smooth decrease on cooling through TC where two-phase ﬂuctuations and vibronic superexchange retain Mn–O bond-length ﬂuctuations. However, on cooling through the ﬁrst-order transition at TOO , a phonon contribution to κ(T ) is restored as a result of orbital and charge ordering in the FI phase. The x = 1/8 phase below TOO appears to have a charge commensurability; where the transition at TOO is second-order (0.14 x 0.16), the phonons are only restored at the lower transition temperature TLO of ﬁg. 43 where charge commensurability probably occurs. In the x = 0.14 sample, a TJT ≈ TC masks the jump in κ(T ) on cooling through TJT . In the x = 0.16 sample, κ(T ) is suppressed in the orbitally ﬂuctuating O* phase above TC , but it increases on cooling through TC into the FM phase where the electrons become itinerant rather than vibronic. However, on cooling through the insulator-metal transition at TIM , κ(T ) is again suppressed, which contrasts with cooling through TOO in x = 0.12. In the x = 0.17 crystal, spin-lattice interactions suppress κ(T ) above TC , see ﬁg. 19 (Zhou and Goodenough, 2002a); the decrease in κ(T ) on cooling below 110 K is due to the appearance of two-phase ﬂuctuations, see ﬁg. 43. There is also a drop in κ(T ) on cooling through TOR ; the rhombohedral phase does not support any orbital ﬂuctuations within the metallic matrix. Note the change of scale for the x = 0.19 crystal where κ(T ) exhibits a strong phonon component below TC . These data demonstrate the utility of monitoring κ(T ) to determine the existence of bond-length ﬂuctuations. Figure 48 extends the phase diagram of La1−x Srx MnO3 to include the region 0.2 x 1.0. Optical studies of the ferromagnetic ground state of single-crystal samples with 0.15 x 0.4 have revealed that the low-energy optical conductivity changes with decreasing x from Drude-like for x > 0.2 to incoherent broad features for x < 0.2 with spectral weight transferred to the mid-infrared region (Saitoh et al., 2000). Temperature-dependent reﬂectivity spectra on a single-crystal x = 0.175 sample showed a crossover with decreasing temperature from incoherent to coherent behavior (Takenaka et al., 1999, 2000). Analysis of the relaxation of the uniform-precession magnons into other spin-wave modes in an electronspin-resonance (ESR) experiment on x = 0.33 samples did not require the introduction of magnetocrystalline anisotropy or chemical inhomogeneities; the data could be ﬁt to a model in which the relaxation was due to demagnetizing ﬁelds at pores or between grains in polycrystalline materials or from surface irregularities in single crystals (Rivadulla et al., 1999b). Vasiliu-Doloc et al. (1998b) have used cold-neutron triple-axis measurements of single-crystal x = 0.2 and 0.3 samples to investigate the long-wavelength spin dynamics. They found that both systems behave like isotropic ferromagnets at low temperatures. However, an anomalously strong quasielastic central peak develops and dominates the ﬂuctuation spectrum as T → TC . It appears that the coexistence of spin-wave excitations and spin diffusion is a common characteristic in manganese-oxide perovskites and may be related to phase ﬂuctuations responsible for the CMR phenomenon. These data are consistent with earlier studies of the magnetization M(T ) in the FM phase near x = 0.3 that showed a decrease of M(T ) with increasing temperature compatible with spin-wave excitations (Smolyaninova et al., 1997) but the spin dynamics near TC showed evidence of strong electron-lattice interactions (Fernández-

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Fig. 48. Phase diagram of La1−x Srx MnO3 , 0 x 0.7, after Zhou and Goodenough (2001a); B. Dabrowski (private communication).

Baca et al., 1998). The volume of an x = 0.3 sample showed a smooth contraction on cooling through TC (Martin et al., 1996). Several research groups place the boundary between the FM and AFM phases beyond x = 0.5; this boundary varies sensitively with the method of sample preparation. Fujishiro et al. (1998) place it in the range 0.48 < x < 0.50. As discussed in more detail in sect. 3.7, several phases compete with one another in the R0.5 A0.5 MnO3 samples (R = lanthanide, A = alkaline earth), the more stable varying with the tolerance factor t. In the R1−x Srx MnO3 system, a relatively large tolerance factor stabilizes a competition between the FM phase with 3D itinerant electrons and a type-A AFM phase in which the occupied e orbitals become ordered into the (001) planes to give 2D itinerant electrons in these planes and antiferromagnetic superexchange coupling between planes as in the type-A (CAFI) insulating phase in LaMnO3 . Dho et al. (2001) investigated the thermal hysteresis of magnetization and resistivity at TN in the range 0.5 x 0.6. They observed a normal counter-clockwise hysteresis (TN higher on heating, lower on cooling) for the magnetic transition, but the resistivity ρ(T ) showed an anomalous clockwise thermal hysteresis in the compositional range where a TN < TC is found. From these experiments, it is apparent that a two-phase region extends either side of the magnetic AFM-FM transition temperature TN . As the tolerance factor increases with x to t = 1, the room-temperature symmetry changes from orthorhombic to rhombohedral to tetragonal to cubic. With x 0.8, a t > 1 stabilizes a

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hexagonal polytype, but the cubic phase may be obtained by quenching a reduced LaMnO3−δ to room temperature and then oxidizing at lower temperatures. A type-C antiferromagnetic order reported for the range 0.65 < x < 0.95 includes two-phase regions on either sides of a narrower single phase, but the boundaries of the ﬂuctuating two-phase regions have not been mapped. The type-C antiferromagnetic order, table 1, consists of ferromagnetic Mn–O– Mn chains along the c-axis with antiferromagnetic coupling between the chains. This type of magnetic order reﬂects an ordering of the e electrons into a 1D c-axis majority-spin σ ∗ band below TN that is occupied by (1 − x) electrons per formula unit; the 1D band may support a charge-density wave. 3.6. The system La1−x Cax MnO3 The relative stabilities of the competing phases in the manganese-oxide perovskites depend critically on the tolerance factor t, which is smaller in the La1−x Cax MnO3 system than in La1−x Srx MnO3 . A smaller t generates a greater bending of the (180◦ − φ) Mn–O–Mn bond, and the R-rhombohedral phase is only found at higher temperatures. The O* –R transition temperature TOR of the phase diagram of ﬁg. 49 is taken from Uehara et al. (private communication) and Cheong and Chen (1998). Early studies of the properties of the system were plagued by a variable oxygen stoichiometry, particularly for compositions with smaller x. Dabrowski et al. (1999b, 1999c) have made a careful study of the conditions under which cation vacancies are formed and their inﬂuence on the physical properties of the La1−x Cax MnO3 system. As in the La1−x Srx MnO3 system, the O –O* transition at TJT decreases sharply with x. Although the disproportionation reaction occurring at TJT in LaMnO3 is retained at smaller values of x, it is found at a TD > TJT . Unlike the La1−x Srx MnO3 system, the concentration of mobile small polarons and the activation energy of their mobility change little at TJT . Therefore, TJT is not tracked by monitoring the resistivity, but by following the evolution with x of the O –O* structural transition or the associated speciﬁc-heat anomaly. The O* phase is pseudocubic, but the MnO6/2 octahedra are rotated ca. 20◦ about the b-axis (space group Pbnm) relative to the ideal cubic-perovskite structure √ (Faaland et al., 1998) and locally cooperative Jahn–Teller deformations sustain a c/a ≈ 2. High-resolution neutron powder diffraction (Radaelli et al., 1996, 1997a; García-Muñoz et al., 1997) extended X-ray absorption ﬁne structure (EXAFS) (Subías et al., 1998) and optical-conductivity spectra (Jung et al., 1998) have established the presence of dynamic distortions of the MnO6/2 octahedra in the O* phase above TC and a dramatic suppression of these distortions in the ferromagnetic metallic (FM) phase below TC . Above TN or TC , the conductivity of the O and O* phases ﬁt the adiabatic dielectric-polaron model α = (A/T ) exp(−Ea /kT ) over the entire doping range (Worledge et al., 1998). However, thermoelectric-power data show that the charge carriers evolve from small polarons to two-manganese Zener polarons with increasing x (see discussion of ﬁg. 31). These polarons are to be distinguished from the second phase into which they progressively condense on cooling as a result of a spinodal phase segregation into hole-rich ferromagnetic, vibronic (FV) clusters within a paramagnetic O or O* matrix. (These clusters are mistakenly referred to as conventional magnetic polarons in some of the literature.) The speckled area of ﬁg. 49 denotes the spinodal region, but this region has not been systematically mapped by experiment.

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Fig. 49. Temperature – x phase diagram of La1−x Cax MnO3 .

The hole-rich clusters grow with x and with decreasing temperature; and below a critical temperature Tsp > TN or TC , they become superparamagnetic FV clusters. An external magnetic ﬁeld stabilizes the FV phase relative to the paramagnetic matrix in the interval TC < T < Tsp ; and where the clusters grow to beyond percolation in the applied ﬁeld, the resistance drops to give a “colossal negative magnetoresistance”, which is known as the CMR phenomenon. Moreover, the volume fraction of the FV phase grows to beyond percolation on cooling to a TC > TN , and a ﬁrst-order phase change occurs at TC due to a discontinuous increase in the volume fraction of the FV phase in the internal molecular ﬁeld present below TC . As the volume fraction of the FV phase at a given T grows with increasing x, TC increases until the magnetic transition at TC becomes second-order. The initial substitution of Ca for La is charge-compensated by the introduction of Mn(IV) ions that, at lower temperatures, become trapped at one of the 8 nearest neighbors to a Ca2+ ion (Matsumoto, 1970b; Alonso et al., 2001). Elastic and inelastic neutron scattering have indicated that by x = 0.05, hole-rich ferromagnetic droplets form within the CAFI matrix with a correlation length ξ ≈ 8–10 Å (Hennion et al., 1997). Local ferromagnetic order only requires an inversion of the c-axis interactions within a droplet, which can occur for hole-rich droplets. The existence of ferromagnetic clusters within the CAFI O matrix was found below TN over the range 0.05 x 0.10 with evidence that the phase segregation extends into the paramagnetic phase (Moussa et al., 1999). Direct evidence for phase segregation above as well as below TC or TN in the interval 0.05 x 0.3 has also been found with Mössbauer

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spectroscopy (Chechersky et al., 1997, 1999a, 2001; Nath et al., 2000; Hannoyer et al., 2000) and Mn K-edge EXAFS (Lanzara et al., 1998). Allodi et al. (1997, 1998a), Papavassiliou et al. (1999), and Dho et al. (1999a) have used 139 La and 55 Mn NMR to show the growth of the volume fraction of a ferromagnetic phase in the paramagnetic matrix with increasing x. Heffner et al. (2001) used muon-spin-relaxation measurements on a series of samples in the range 0 x 0.10; fast relaxation rates were assigned to the ferromagnetic regions, which is consistent with FV behavior, and a slow Mn relaxation rate to the antiferromagnetic matrix. Markovich et al. (2002) employed several techniques on an x = 0.18 single crystal to demonstrate the existence of a ferromagnetic second phase both above and below TC and growth of the ferromagnetic volume fraction not only in an applied magnetic ﬁeld, but also under hydrostatic pressure. Hydrostatic pressure stabilizes the phase of smaller volume, which indicates the ferromagnetic phase has vibronic σ -bonding states, i.e., it is an FV phase, whereas the matrix contains localized electrons in orbitally ordered states. However, the CMR phenomenon only occurs where the volume fraction of the ferromagnetic FV phase approaches percolation in the paramagnetic phase and achieves percolation on cooling through a TC > TN (Biotteau et al., 2001). On the other hand, Congeduti et al. (2001) found, with Raman spectroscopy from a polycrystalline x = 0.25 sample, an abrupt transition at ca. 7.5 GPa to an orbitally ordered phase, and Meneghini et al. (2002) monitored the resistance of the same sample to show that the transition prevents transformation under pressure from the FV to the FM phase. Although pressure increases the tolerance factor, the FM phase was not reached because pressure also stabilizes orbital order, but probably as an ordering of two-manganese Zener polarons as in the low-temperature O phase of the La1−x Srx MnO3 system. The transition to poorer conductivity at higher pressures was also noted by Okuda et al. (2000) and by J.-M. Li et al. (2001). On cooling through TC in the range 0.10 x 0.30, there is a ﬁrst-order volume contraction associated with a discontinuous increase in the volume fraction of the more conductive FV and FM phases (Radaelli et al., 1996; Huang et al., 1998) where electrons tunnel from Mn(III) to Mn(IV) neighbors in a time τh ωo−1 . In contrast, the transition from the paramagnetic phase to the CAFI phase at TN is second-order with a smooth evolution of the volume. The charge carriers in the CAFI matrix remain polaronic. On cooling through TC in the range 0.25 x 0.45, the FV phase changes to the ferromagnetic metallic (FM) phase, but no study has been made of whether this transition is ﬁrst-order as in La1−x Srx MnO3 . However, Lynn et al. (1996), Erwin et al. (1997), and Dai et al. (2000) have used inelastic neutron scattering to study the evolution with temperature of the spin dynamics in the ferromagnetic phase; they found that the FM phase behaves as an ideal isotropic ferromagnet at low temperatures, but it develops an anomalous spin-diffusion component above ca. 200 K that progressively dominates the spin-ﬂuctuation spectrum as the temperature increases to TC . This behavior signals a transition from the FM toward the FV state as T increases to TC . Dai et al. (2001) also studied the evolution of diffuse scattering from magnetic and lattice ﬂuctuations in single-crystal x = 0.15, 0.20, and 0.30 compositions. The x = 0.30 sample showed an unambiguous transition to a FM phase on cooling through TC whereas the x = 0.15 and 0.20 crystals exhibited a transition on cooling through TC to a phase with strong electron-lattice interactions, which we identify with the FV phase. The FV-FM transition occurs near the crossover of TJT and TC

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(a)

(b)

Fig. 50. Type-CE antiferromagnetic order in a–b planes; antiferromagnetic coupling above c-axis in space group Pbnm; (a) ordering of localized occupied e orbitals after Goodenough (1955), and (b) ordering of Zener polarons.

in the range 0.20 < x < 0.25, which is at a higher x than in the La1−x Srx MnO3 as expected for smaller tolerance factor t. As in the La1−x Srx MnO3 system, the percolating conductive FV matrix containing an antiferromagnetic second phase converts to a ferromagnetic-insulator (FI) phase below a TOO in the compositional range 0.10 < x < 0.25. A sound-velocity anomaly at TOO and at TC allows tracking of these temperatures vs. x (Fujishiro et al., 1999). Transport measurements (G. Zhao et al., 2000; Hong et al., 2001) have revealed polaronic conduction in the FI phase, but not in the FM phase. The coexistence of two competing phases sensitive to light, to external magnetic or electric ﬁelds, and to pressure has led to many studies by a variety of techniques of the peculiar properties of samples in the range 0.10 x 0.35 (Ilisavskii et al., 2001; Fisher et al., 2001; Gordon et al., 2000; Gordon et al., 2002; Cordero et al., 2002; Ren et al., 2001; Hudspeth et al., 2002; Zuo and Tao, 2001; Reutler et al., 2000; Raquet et al., 2000; Zhu et al., 1999; Hueso et al., 1999; Causa et al., 1998; Kumar et al., 2002; Lobad et al., 2001; Mayr et al., 2001; Yoon et al., 1998; Papavassiliou et al., 2001; Huhtinen et al., 2000; Yuzhelevski et al., 2001). On the opposite side of the maximum in TC vs. x at x = 3/8, the FM phase competes with a type-CE antiferromagnetic phase having the magnetic and charge order of ﬁg. 50(a). In the range 0.4 < x 0.5, the FM and type-CE phases coexist (Moritomo, 1999). The phase diagram shows a TCO < T < TC . Here also an external magnetic ﬁeld stabilizes the conductive FM phase relative to the type-CE antiferromagnetic-insulator (AFI) as is illustrated in ﬁg. 51 for Nd0.5 Sr0.5MnO3 (Shimomura et al., 1999). The metamagnetism of the CE phase provides another type of CMR phenomenon.

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(b)

Fig. 51. (a) Temperature dependence of the resistivity ρ(T ) of Nd0.5 Sr0.5 MnO3 under various magnetic ﬁelds. (b) Temperature-ﬁeld phase diagram; after Shimomura et al. (1999).

Whereas the type-CE AFI phase competes with the FM phase in the range 0.4 < x 0.5 of La1−x Cax MnO3 , reduction of the tolerance factor by substitution of Pr for La in La5/8−x Prx Ca3/8 MnO3 introduces already at small x a charge-ordered second phase (Kim et al., 2000a); Pr5/8 Ca3/8 MnO3 undergoes charge ordering below a TCO ≈ 225 K that becomes an AFI phase below a TN ≈ 175 K (Dediu et al., 2000). In this sample, the Curie temperature of any FM minority phase is TC < TCO . The (La1−y Pry )0.67Ca0.33 MnO3 system shows a similar percolation transition from a FM for y = 0 to an orbital and charge-ordered insulator for y > 0.75, see sect. 3.4; the volume fraction of the conductive, ferromagnetic phase grows on lowering the temperature (Kim et al., 2000a; Dediu et al., 2000; Uehara et al., 1999; Podzorov et al., 2000; Babushkina et al., 1999). Smolyaninova et al. (2002) have studied the inﬂuence of isotope exchange on a number of samples in the La1−x Cax MnO3 and (La1−y Pry )0.67Ca0.33 MnO3 systems. The most prominent isotope shift of the transition temperatures is in the two-phase compositions; the two-phase ﬂuctuations are thus shown to be accommodated by cooperative, dynamic oxygen displacements perpendicular and/or along the (180◦ − φ) Mn–O–Mn bond axes. The predicted charge and orbital ordering of ﬁg. 50(a) for the CE phase (Wollan and Koehler, 1955; Goodenough, 1955) was thought to be fully corroborated (Radaelli et al., 1995, 1997b). However, as discussed in detail in sect. 3.7 for the R0.5 A0.5 MnO3 compositions, it is necessary to distinguish the type-CE phase appearing below a TN TCO < TC

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from that stabilized below a TN < TCO where the Curie temperature for the competing FM phase is TC < TCO . Rivadulla et al. (2002) predicted that the charge and orbital ordering of ﬁg. 50(a) occurs where there is a TCO > TC , but that the ferromagnetic zig-zag chains contain the two-manganese Zener pairs of ﬁg. 50(b) where a dominant FM phase makes TC > TCO . La0.5 Ca0.5 MnO3 has a TN TCO < TC , and a recent single-crystal neutron-diffraction study (Daoud-Aladine et al., 2002) has shown independently that indeed the CE phase below TN contains the ordering of Zener polarons indicated in ﬁg. 50(b). However, the competition in La0.5 Ca0.5 MnO3 between the FM phase with TC > TCO and the charge-ordered phase with TCO > TC is made complicated by an extreme sensitivity of the critical temperatures and the respective volume fractions on the oxygen stoichiometry (Y.G. Zhao et al., 2002; Levy et al., 2000), the grain size of the polycrystalline samples (Levy et al., 2000; Freitas et al., 2002), and thermal cycling (Uehara and Cheong, 2000) as well as on the Ca concentration x. A variety of techniques have been used to characterize this situation. Huang et al. (2000) examined with neutron diffraction three polycrystalline samples with x = 0.47, 0.50, and 0.52. They reported single-phase paramagnetic materials with a spinodal phase segregation occurring below a ﬁrst-order orbital-ordering (OO) transition at TOO < TC . In the interval TOO < T < TC , the FM phase coexisted with a paramagnetic phase that underwent the ﬁrst-order transition at TOO . The x = 0.47 sample had a TC = 265 K and a TOO = 230 K. The OO phase had the smaller volume fraction, and the volume fraction of the FM phase increased on the formation of the OO phase. Below a Néel temperature TN = 160 K of the OO phase, the diffraction peaks sharpened and the structure could be indexed as that of the type-CE AFI phase. The volume fraction of the FM phase remained 0.6 to lowest temperatures in the x = 0.47 sample; it decreased with increasing x, but was still present as a minority phase in the x = 0.52 sample. However, a diffraction experiment does not detect phase ﬂuctuations that may be occurring in the paramagnetic phase above TC . Kim et al. (2000b) noted a suppression of the conductivity σ (T ) and of the phonon component of the thermal conductivity as well as a broadening of the diffraction peaks to temperatures as high as 900 K, and Naler et al. (2002) used inelastic light scattering to show strong ﬂuctuation effects persisting in an x = 0.50 sample to at least 2TOO . In another experiment, Kim et al. (2002) used optical spectroscopy to monitor the gap Δ that is opened at the Fermi energy by stabilization of the CE AFI phase. They found a 2Δ/kTOO ≈ 30 for x = 0.5 that decreased rapidly with increasing x even though TOO had a broad maximum at about x = 0.62. They also noted that an optical pseudogap is present well above TCO , setting in below a T ∗ ≈ 600 K where independent evidence for phase ﬂuctuations had been found. The existence of two-phase ﬂuctuations persisting well into the paramagnetic temperature range appears to be well-established. The coexistence of the two phases to lowest temperatures near x = 0.5 has also been demonstrated indirectly by ultrasonic sound velocity (Zheng et al., 2001) as well as by magnetization and conductivity measurements (Y.G. Zhao et al., 2002; Levy et al., 2000; Xiao et al., 1996; Schiffer et al., 1995; Roy et al., 1998, 1999) and more directly by 119Sn and 57 Fe Mössbauer spectroscopies (Simopoulos et al., 2001; Kallias et al., 1999), electron diffraction (Chen and Cheong, 1996; Mori et al., 1998a), NMR (Dho et al., 1999b; Allodi et al., 1998b, 2000; Yoshinari et al., 1999; Papavassiliou et al., 1997), and infrared (Liu et al., 1998) spectroscopies. Mori et al. (1998a) showed that in their x = 0.5 sample the length scale of the two

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phases increased on cooling from 100–120 Å at 200 K to 500–600 Å at 125 K before converting below 95 K to an OO type-CE AFI matrix. The critical magnetic ﬁeld for conversion of the metamagnetic CE AFI phase to the FM phase was found to be about 8 T on increasing an external magnetic ﬁeld H and 3 T on lowering the ﬁeld (Freitas et al., 2002). Moreover, Huang et al. (2000) reported that the volume fraction of the FM phase increased more for a given H ﬁeld if the sample was cooled in the magnetic ﬁeld than if warmed in that ﬁeld after cooling in zero ﬁeld. Uehara and Cheong (2000) showed that the extent of the ﬁrst-order conversion from one phase to another in an applied ﬁeld depends on the rate of cooling or heating and on aging to relieve the internal stresses associated with the volume changes that occur; the phase transition is not martensitic. The electron-diffraction study of Chen and Cheong (1996) revealed domains of incommensurate charge ordering in the FM matrix in the range TOO < T < TC with a ﬁrst-order change at TOO to long-range ordering of the commensurate OO phase below TOO . The existence of two phases was not due to any inhomogeneity in the Ca-ion distribution and did not appear to be due to a segregation into hole-rich and hole-poor domains; it reﬂects a competition between orbital order and disorder similar to that found in LaMn0.5Ga0.5 O3 . Dark-ﬁeld images at 95 K showed CE domains a few thousand angstroms in diameter separated by twin boundaries parallel to a Mn–O–Mn bond axis. The OO phase was found (Smolyaninova et al., 1998) to have a large excess speciﬁc heat compared to the FM phase; this excess entropy can only originate from excitations of nonmagnetic origin. Application of a magnetic ﬁeld of 8.5 T, which transformed the resistivity to a metallic temperature dependence, left the speciﬁc heat unchanged with no evidence of a kT term from mobile charge carriers. The mobile charge carriers apparently remain strongly coupled to the oxygen vibrations and therefore behave as vibrons. Further evidence of the strong electron coupling to the oxygen vibrational modes comes from 18 O/16 O isotope exchange, which increases TCO of La0.5 Ca0.5 MnO3 by 9 K in zero magnetic ﬁeld (Zhao et al., 1999) and of Nd0.5Sr0.5 MnO3 by 21 K (Mahesh and Itoh, 1999). Raman spectra show an anomalous softening of the 494 cm−1 and 604 cm−1 modes below TCO (Granado et al., 1998). The two-manganese Zener polarons appear to order in a charge-ordered (CO) phase in the range 0.5 < x 0.75. Mori et al. (1998a, 1998b) have observed in thin ﬁlms planes of a La0.5 Ca0.5 MnO3 -type phase alternating with planes of a CaMnO3 -type phase, see ﬁg. 52, in a series of x = n/(n + 2) planes, where n is the number of Mn(IV) planes in the CaMnO3 slab. On the other hand, high-resolution synchrotron X-ray and neutron powder diffraction on bulk x = 0.67 samples suggested an ordering of Mn3+ ions separated as far apart as possible in the basal planes (Radaelli et al., 1999; Fernández-Díaz et al., 1999); however, such a “Wigner crystal” model is inconsistent with the formation of Zener polarons, which can be accommodated in the model of Mori et al. (1998a, 1998b). The superlattice reﬂections of the CO phase for x = 0.80 were noticeably broader than those of the lower-x compositions (Chen and Cheong, 1996; Chen et al., 1997; Li et al., 1999). Therefore Pissas et al. (2002) used powder neutron diffraction to study whether charge ordering was actually present in x = 0.80 and 0.85 samples. They found a transition from the O* -orthorhombic paramagnetic phase to a monoclinic P 21 /n antiferromagnetic phase containing two distinguishable Mn sites below a TN = TOO = 210 K for x = 0.80 and 160 K for x = 0.85; the low-temperature data showed ferromagnetic Mn–O–Mn chains coupled antipar-

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Fig. 52. Charge and orbital ordering in the orthorhombic basal plane for (a) x = 0, (b) x = 0.5 for localized e orbitals, and (c) Mori et al. (1998a, 1998b) model for x = 2/3.

allel to one another (type-C antiferromagnetic order of table 1) with the magnetic moment of ca. 2.5μB oriented along the chains. They found no evidence of charge ordering as Mn(III) ions, but the magnetic order signals an ordering of the e electrons into the ferromagnetic chains. A contraction of the Mn–O bonds along the ferromagnetic chains on cooling through TN implies, therefore, an ordering of the e electrons along the c-axis above TN ; the contraction can then be understood from the virial theorem if the transition at TN involves a transition from localized e to 1D itinerant σ∗ electrons along the chains; these electrons appear to stabilize, in addition, a commensurate charge-density wave. The reduction in the magnitude of the measured magnetic moment on the Mn atoms is characteristic of antiferromagnets. 3.7. R0.5 A0.5 MnO3 The R0.5 A0.5 MnO3 compositions with A = alkaline earth have a ﬁxed ratio Mn(IV)/Mn(III) = 1, but it is possible to pass from localized to itinerant electronic behavior on the MnO3 array by varying the mean size of the A-site cations and hence the geometric tolerance factor t. In this family, the evolution of the competing phases at the crossover tolerance factor t = tc is made complex by the existence of charge and orbital ordering of localized electrons competing with ordering of Zener pairs in the crossover region t = tc ± Δt. In addition, an orbital ordering at t = tc + Δt constrains itinerant σ ∗ electrons to the (001) planes to give a type-A antiferromagnetic metallic (AFM) phase that competes with ordering of Zener pairs in a type-CE AFI phase on one side and a FMM phase on the other side that has 3D itinerant σ ∗ electrons. Several groups have presented temperature vs. tolerance factor phase diagrams (Rivadulla et al., 2002; Kuwahara and Tokura, 1998; Rao et al., 1998; Damay et al., 1999; Krupicka et al., 1999). Kuwahara and Tokura (1998) and Rivadulla et al. (2002) had stoichiometric singlecrystal data and were the only groups to recognize the existence of a critical tolerance factor tc separating localized from itinerant electronic behavior; their two phase diagrams are shown in ﬁg. 53. Tokura et al. (1996) were also the ﬁrst to report the existence of a narrow, ferromag-

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Fig. 53. Temperature-tolerance factor phase diagrams for R0.5 A0.5 MnO3 from (a) Kuwahara and Tokura (1998), and (b) Rivadulla et al. (2002). In (a), PI = paramagnetic insulator, COI = charge-ordered insulator, FM = ferromagnetic metal. In (b), SP = superparamagnetic, SRCO = short-range charge-ordered ﬂuctuations, I = CE AFI of ﬁgs. 50(a) and 52(b), II = ferromagnetic metal (FMM), FMV = ferromagnetic vibronic, PM = paramagnetic, III = CE AFI of ﬁgs. 50(b) and 57, IV = Type-A antiferromagnetic metal (AFM), V = FMM; shaded boundaries are estimates.

(a)

(b)

Fig. 53. Continued.

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netic metallic (FMM) phase inserted between two antiferromagnetic type-CE insulator phases that they identiﬁed as COI in their diagram. They made no distinction between the two COI phases as they assumed the type-CE antiferromagnetic order necessarily implied a charge ordering as Mn(III) and Mn(IV) ions. Therefore, they considered the FMM phase to represent a metastable state appearing at a quantum critical point (QCP) where two-phase ﬂuctuations suppress not only charge order (CO), but also orbital order (OO) and magnetic order. But such a critical point occurs at a crossover from localized to itinerant electronic behavior, so the assumption that the two CE AFI phases either side of t = tc both contain CO turns out to be invalid. Burgy et al. (2002) have modeled the QCP behavior by introducing quenched disorder into the Hamiltonian describing the competition between the COI and FMM phases. Rivadulla et al. (2002) chose to study the system Pr0.5(Ca1−x Srx )0.5 MnO3 having a smaller variance σ 2 of the A-site-cation sizes; they found a stable FMM phase of larger volume at the critical tolerance factor tc . We interpret the more complete phase diagram of ﬁg. 53(b) within the framework of a transition from localized to itinerant electronic behavior in the range 0.972 < t < 0.992 that includes t = tc ≈ 0.975. (We calculate t using 12-fold coordination of the A-site cations.) Although such a transition is ﬁrst-order in accordance with deduction from the virial theorem, nevertheless orbital ordering and cooperative bond-length adjustments allow it to occur in steps, beginning with the formation of molecular orbitals within two-Mn Zener polarons, transforming next to 1D metallic chains and then to 2D metallic planes before 3D itinerantelectron behavior is achieved. In the R0.5 A0.5 MnO3 family, the 1D itinerant-electron chains are replaced by a charge-density-wave zig-zag chain of ordered Zener polarons. Above Tsp of ﬁg. 53(b), the paramagnetic susceptibility has Curie–Weiss behavior with a Weiss constant θ > 250 K, which is indicative of ferromagnetic exchange interactions where there are orbital ﬂuctuations and/or Zener double exchange. A deviation of the susceptibility from Curie–Weiss behavior on cooling below Tsp is characteristic of short-range ferromagnetic order or the onset of superparamagnetism. The thermoelectric-power data α(T ) indicate the presence of about 20% two-Mn Zener polarons, which would have a strong ferromagnetic double-exchange coupling within a pair. We therefore conclude that ferromagnetic order within Zener polarons gives rise to superparamagnetism below Tsp . This phenomenon is characteristic of all compositions in a range of t spanning the critical tolerance factor tc ≈ 0.975. On cooling samples with t < 0.972, a charge-ordering transition occurs at TCO ≈ 225 K; an orbital ordering below TOO is accompanied by the onset of type-CE antiferromagnetic order below a TN = TOO ≈ 160 K. In this phase I of ﬁg. 53(b), a CO of Mn(III) and Mn(IV) ions breaks up the Zener pairs to stabilize localized electrons. Therefore, the orbital and charge ordering of this CE AFI phase is expected to have the classical (Goodenough, 1955) localizedelectron order of ﬁg. 50(a). Samples with t 0.992 are metallic ferromagnets (FMM) below TC to lowest temperatures, phase V. Between phases I and V there is a transition from localized to itinerant electrons of e-orbital parentage. The transition temperatures TCO for the CO phase and TC for the FM phase cross at the critical tolerance factor tc ≈ 0.975 where a unique FMM phase II appears. As can be seen in ﬁg. 54, the room-temperature volume of phase II is larger than anticipated for a smooth evolution of unit-cell volume with increasing t; at t = tc with Mn(IV)/Mn(III) = 1, A-cation

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Fig. 54. Evolution of the room-temperature volume vs. tolerance factor of single-crystal Pr0.5 (Ca1−x Srx )0.5 MnO3 (open circles) after Rivadulla et al. (2002), and (Nd1−x Smx )0.5 Sr0.5 MnO3 (closed triangles) after Kuwahara et al. (1997).

displacements apparently stabilize a larger volume so as to straighten the Mn–O–Mn bond angle sufﬁciently to give an effective tolerance factor teff 0.992. Comparison of ﬁgs. 53(a) and (b) shows that a larger variance σ 2 of the A-site-cation size suppresses TC of phase II and, indeed, may suppress all order to lowest temperatures. Rivadulla et al. (2002) have shown that small deviations from unity of the Mn(IV)/Mn(III) ratio and hydrostatic pressure also suppress phase II. Near t = 0.980, there is a discontinuous change in TC ; by analogy with the transition at x = 0.15 in La1−x Srx MnO3 , this discontinuity probably represents a change from vibronic to itinerant electronic behavior in the ferromagnetic phase, i.e., FMV to FMM. Vibronic conduction occurs where there are cooperative bond-length ﬂuctuations associated with the coexistence of two phases, a minority paramagnetic (PM) phase that undergoes a CO transition below TCO and a majority FMV phase having a TC > TCO . The FMM phase II appearing at t = tc is single-phase. On lowering the temperature in the range 0.980 < t < 0.992, the FMM phase transforms completely, or partially, to a type-A antiferromagnetic metallic (A AFM) phase IV in which orbital order constrains itinerant σ ∗ electrons and de Gennes double exchange to the (001) planes; the interactions between (001) planes are antiferromagnetic by t3 –O–t3 superexchange as occurs in LaMnO3 where all the 3d electrons at Mn(III) remain localized. In the range 0.972 < t < 0.980, the competition between stable phases is greatest; this competition results in the coexistence of two ﬂuctuating phases. The phase ﬂuctuations may suppress all long-range order at t = tc or, if the atomic displacements become static, may stabilize a unique single phase having 3D itinerant electrons of e-orbital parentage in a single FMM phase, phase II. The suppression of all long-range order corresponds to QCP behavior. QCP behavior or the appearance of phase II of larger volume at t = tc occurs at the crossover from a minority FMV phase in a majority CO matrix to a minority CO phase in a majority

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Fig. 55. Effects of hydrostatic pressure on the temperature dependence of the thermoelectric power α(T ) for Pr0.5 (Ca0.9 Sr0.1 )0.5 MnO3 , after Rivadulla et al. (2002).

FMV matrix. Although pressure increases t in the crossover region because of the larger compressibility of the Mn–O bond where it has a double-well equilibrium bond length, it was not possible to obtain the higher volume FMM phase II by applying pressure to a t = 0.973 < tc sample (Rivadulla et al., 2002). Figure 55 shows the evolution with pressure of the thermoelectric power α(T ); a crossover from a TCO > TC at 8.7 kbar to TC > TCO at 15.4 kbar is evident, crossover occurring near 13 kbar (ﬁg. 56). In this experiment, the magnitude of α(T ) increases in the CO insulator phase and decreases in the conductive FMV phase. This situation indicates that a distinction must be made between the CE AFI phase I below TN = TOO and the CE AFI phase III appearing below TN = TOO . Whereas the classical model of ﬁg. 50(a)

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Fig. 56. Evolution with pressure of the critical temperatures for Pr0.5 (Ca0.9 Sr0.1 )0.5 MnO3 , after Rivadulla et al. (2002).

should apply to phase I, phase III appears on the itinerant-electron side of tc and represents the next step in the break-up with decreasing bandwidth from 3D to 2D σ ∗ bands to Zener polarons. Therefore phase III was predicted to represent an ordering of Zener polarons (Rivadulla et al., 2002). Independent direct evidence for such an ordering in a CE AFI phase has been provided by Daoud-Aladine et al. (2002) with neutron diffraction on a Pr0.6Ca0.4 MnO3 crystal; on lowering t, the 2D (x 2 − y 2 )σ ∗ bands of the type-A AFM phase IV breaks up into the charge-density-wave pattern of ordered Zener polarons shown in ﬁg. 57. The competition between the FMM phase and paramagnetic CO phase is already manifest in phase I where a modest applied magnetic ﬁeld stabilizes the FMM phase relative to the CO paramagnetic phase. Figure 58 shows typical magnetization, M(T ), resistivity, ρ(T ), and thermoelectric power, α(T ), curves for Pr0.5 (Sr0.9 Ca0.1 )0.5 MnO3 (t ≈ 0.973). The sharp drop in M(T ) for H = 0 on cooling through TCO ≈ 225 K reﬂects a break-up of the superparamagnetic Zener polarons in the CO phase I, and the smaller maximum in M(T ) at TN = TOO = 150 K marks the onset of the CE AFI magnetic and orbital order. The thermal hysteresis in the ρ(T ) curve (inset) shows that the transition at TCO is ﬁrst-order and therefore cannot be described as a simple order–disorder transition. The α(T ) curve is temperatureindependent above TCO , which is characteristic of polaron conduction; and from eq. (26), α = −28 μV/K corresponds to about 20% Zener polarons above TC . The abrupt increase in the magnitude of α(T ) on cooling through TCO and TN = TOO is due to a progressive trapping out of mobile electrons with increasing charge ordering. The maximum in |α(T )| appears to correspond to a growth with decreasing T in a conductive FM minority phase below 100 K. Figure 58(b) shows the change in M(T ) in an applied magnetic ﬁeld in the range 3 T H 5 T. In an H = 4.5 T, long-range CO is completely suppressed in the range TN < T < TCO for H = 0; the saturation magnetization approaches the spin-only 3.5μB /Mn just above TN . However, orbital ordering below TOO = TN stabilizes the CE AFI phase, which

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Fig. 57. Inverse magnetic susceptibility 1/χ (T ) of Y0.5 Ca0.5 MnO3 and schematic picture of the magnetic state: (a) PM above TCO with formation of Zener polarons setting in below 450 K; (b) PM Zener polarons order between TCO and TN ; (c) CE AFI structure below TN , after Daoud-Aladine et al. (2002).

probably means it reestablishes the static CO. A similar behavior was found by Kuwahara and Tokura (1998) in Pr0.5 Ca0.5 MnO3 , but in higher magnetic ﬁelds as a consequence of a smaller tolerance factor t. Like Pr0.5 Ca0.5 MnO3 , Nd0.5Ca0.5 MnO3 corresponds to phase I with TCO = 250 K and TN = TOO = 160 K (Millange et al., 2000). In this compound, ESR data showed no trace of a FM second phase imbedded in the CO phase in zero magnetic ﬁeld (Dupont et al., 2001). Nevertheless, a high-temperature Curie–Weiss paramagnetism with a positive Weiss constant shows ferromagnetic correlations are present above TCO in this compound also. Moreover, a ferromagnetic phase is stabilized by an applied magnetic ﬁeld in the temperature interval TN = TOO < T < TCO . Millange et al. (2000) used neutron diffraction, magnetic susceptibility, and resistivity of polycrystalline samples to study, in particular, the magnetic behavior in the range TN = TOO < T < TCO ; they found the low-ﬁeld susceptibility was typical of an antiferromagnet whereas no magnetic order could be detected by neutron diffraction, which suggests the presence of short-range antiferromagnetic ﬂuctuations. Joshi et al. (2002) found a progressive motional narrowing of their ESR linewidth on heating in the interval TN = TOO < T < TCO and deduced a polaron activation energy Ea = 0.1 eV associated with the orbital ﬂuctuations that suppress the long-range magnetic order. The introduction in zero applied magnetic ﬁeld of microdomain FM clusters at oxygen vacancies or Cr-atom dopants has also been studied in Nd0.5 Ca0.5 MnO3+δ and Nd0.5 (Ca0.5−x Crx )MnO3 (Frontera et al., 2000; Kimura et al., 1999; Machida et al., 2000, 2002; Chang et al., 2002). Pr0.5 Sr0.5 MnO3 corresponds to phase IV with a type-A AFM phase appearing below a TN = TOO < TC (Kawano et al., 1997; Damay et al., 1998; Llobet et al., 1999). In this phase,

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Fig. 58. (a) Temperature dependence of the magnetization M(T ) of Pr0.5 (Ca0.9 Sr0.1 )0.5 MnO3 taken on heating in a ﬁeld H = 10 Oe after cooling in zero ﬁeld (ZFC) and in H = 10 Oe (FC). Inset: Resistivity ρ(T ) on cooling and warming. (b) M(T ) on cooling in ﬁelds of 3 T and 5 T and on cooling and heating in 4 T, after Rivadulla et al. (2002).

the FMM phase is stabilized to low temperatures by an applied magnetic ﬁeld of a few Tesla. Allodi et al. (2000) have shown with 55 Mn NMR that the FM phase develops from zero ﬁeld by the nucleation of microscopic ferromagnetic domains. At the threshold ﬁeld, the NMR spectrum changes discontinuously into that of a homogeneous, fully aligned ferromagnetic state. Substituting smaller rare-earth ions in R0.5 Sr0.5MnO3 increases the A-site variance as well as reducing t. Whereas La0.5Sr0.5 MnO3 is a phase V FMM, Pr0.5 Sr0.5 MnO3 corresponds to phase IV, stabilizing the type-A AFM phase below TN = TOO , and Nd0.5 Sr0.5 MnO3 contains the coexistence of phases III and IV below TN = TOO ≈ 150 K (Kajimoto et al., 1999; Kuwahara et al., 1995), but an insulator-metal transition to the FMM phase is still induced by an

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applied magnetic ﬁeld. Zvyagin et al. (2000) have observed with ultrasonic measurements a signiﬁcant acoustic-mode softening in the FMM phase, which signals the presence of orbital and/or phase ﬂuctuations in the FMM phase. Sm0.5 Sr0.5MnO3 and Gd0.5Sr0.5 MnO3 have a TCO ≈ 250 K > TN = TOO characteristic of t < tc in the two phase region I + II (Shames et al., 2002; García-Landa et al., 1998). A neutron-diffraction study has shown that Tb0.5 Sr0.5MnO3 has the CE AFI magnetic structure of phase I at 10 K (Machida et al., 2001). On the other hand, Ho0.5 Sr0.5MnO3 shows only short-range order below TN = TOO ≈ 90 K as a result of the internal strains associated with the large A-site-cation variance (Autret et al., 2002). The coexistence of two phases in the interval 0.972 < t < 0.980 has been demonstrated by several techniques. For example, Krupicka et al. (2001) found, with 55 Mn NMR, FM inclusions within the CE AFI phase for Pr0.5Ca0.35 Sr0.15 MnO3 whereas they observed a PM phase coexisting with a FM phase just below TC . The volume fraction of the FM phase IV increased with decreasing temperature until it abruptly vanished below TN = TOO ; the CE AFI phase below TN = TOO would be phase III consisting of ordered Zener polarons. The PM phase corresponds to the minority phase having a TCO . A Pr0.5 (Ca0.85Sr0.15 )0.5MnO3 crystal with t = 0.974 probes the two-phase region below TCO at the approach to tc from the localized-electron side. The ρ(T ) curve, inset of ﬁg. 59, shows a TCO ≈ 220 K. However, unlike the t = 0.973 sample of ﬁg. 58, the M(T ) curve

Fig. 59. Magnetization M(T ) in H = 10 Oe after ZFC and FC in 10 Oe (closed circles) and thermoelectric power α(T ) (open circles) for single-crystal Pr0.5 (Ca0.85 Sr0.15 )0.5 MnO3 . Inset: Resistivity ρ(T ) on cooling and warming, after Rivadulla et al. (2002).

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for t = 0.974 in an H = 10 Oe reveals a ferromagnetic minority phase appearing below TC = 210 K. The volume fraction of this phase grows as the temperature is lowered, reaching a percolation threshold at a Tp ≈ 100 K below which M(T ) increases more sharply with decreasing temperature. The ρ(T ) curve shows a change to a lower resistivity below Tp , which is consistent with percolation of a more conductive phase below Tp . The onset of type-CE antiferromagnetic order below TN = TOO ≈ 150 K of the CO phase retards the growth of the FM minority phase and introduces a thermal hysteresis into M(T ) and ρ(T ). The change in α(T ) at TCO is reduced because the volume fraction of the majority phase is reduced; inﬂections in α(T ) are found at TOO = TN and Tp as expected from this model. Figure 60 shows that the ferromagnetic phase is more easily stabilized by a magnetic ﬁeld relative to the CE AFI phase at temperatures T < Tp ; in the t = 0.973 phase, the CE AFI phase remains stable in applied ﬁelds that are strong enough to convert the CO phase to a FM phase in the interval TN = TOO < T < TCO whereas the t = 0.974 crystal has its CE AFI phase less stable relative to the FM phase than the CO phase in the interval TN = TOO < T < TCO . This inversion of the relative stabilities of the two phases relative to a disordering in an applied magnetic ﬁeld as t approaches tc from the localized-electron side is noteworthy; it suggests that the stability of ordering of localized orbitals as against the formation of Zener polarons decreases more rapidly as t approaches tc than the coulombic stabilization associated with ordering of localized Mn(III) and Mn(IV) ions. However, application of an H = 4 T completely

Fig. 60. Effect of an applied magnetic ﬁeld on the magnetization M(T ) of Pr0.5 (Ca0.85 Sr0.15 )0.5 MnO3 . Upper inset: Open circles measured during cooling in H = 1 T after ZFC from 320 K down to 5 K and warming up to 150 K in zero ﬁeld; solid circles measured in the same way after warming up to 210 K. Lower inset: M vs. H at different temperatures T < Tp , after Rivadulla et al. (2002).

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suppresses phase I; this phase is metamagnetic below TN = TOO with an AF-FM insulatorconductor transition occurring at Tp on cooling in H = 2 T whereas the FM phase is retained on heating in H = 2 T to the zero-ﬁeld magnetic transition at TOO = TN . The upper inset of ﬁg. 60 shows two M(T ) curves taken on cooling in a ﬁeld H = 1 T after a rapid ZFC to 5 K and warming to 150 K or to 210 K. After warming to 150 K before H = 1 T is applied, the ﬁeld-cooled (FC) magnetization remains very small (open circles); the crystal remains in the AF state. However, after warming to 210 K before H = 1 T is applied, the FC M(T ) curve (closed circles) increases sharply on cooling through Tp . The metamagnetism of the AF phase at H = 1 T is then seen to require nucleation within it of a FM phase that grows below Tp . Rapid cooling to 5 K in zero ﬁeld apparently does not provide time for the ferromagnetic clusters to nucleate to an irreversible size. Uehara and Cheong (2000) have shown how cooling rate and aging in a magnetic ﬁeld can drastically inﬂuence the volume fraction ratio of FM/CO phases that coexist in a wide temperature interval in the system La5/8−y Pry Ca3/8 MnO3. The lower inset of ﬁg. 60 shows M vs. H hysteresis for 0 H 5 T at three different temperatures after a ZFC. At 10 K, the metamagnetic transition occurs in the interval 2 T H 3 T on increasing H ; it returns to a spin-glass or canted-spin-AF state on decreasing H below 1 T. At 50 K, the metamagnetic transition occurs in the interval 0.5 T < H < 1.5 T in conformity with the upper inset. At 100 K ≈ Tp , the metamagnetic transition occurs at a larger magnetic ﬁeld, 1.5 T < H < 1.8 T on increasing H and returns to a spin-glass or canted-spinAF state at about H = 1 T on reducing H . This remarkable shift conﬁrms that growth of the FM phase at the expense of the AF phase is greatly facilitated below Tp .

Fig. 61. Magnetization M(T ) in H = 10 Oe after ZFC and FC in 10 Oe (closed circles); thermoelectric power α(T ) (open circles) for Pr0.5 (Ca0.8 Sr0.2 )0.5 MnO3 (t = 0.975). Inset: ρ(T ) showing abrupt metal–insulator transition at TC ≈ 215 K, after Rivadulla et al. (2002).

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Figure 61 shows the ZFC and FC M(T ) curves for the FMM phase II, which show a ﬁrstorder transition at TC where the bond-length ﬂuctuations become frozen out to restore the phonon contribution to the thermal conductivity, ﬁg. 62. In the I + II two-phase samples t = 0.973 and t = 0.974, phase II is suppressed and phase ﬂuctuations inhibit phonon formation below TCO or TC . Tokura et al. (1996) applied hydrostatic pressure to the FM phase II of (Nd0.125Sm0.875)0.5 Sr0.5 MnO3 having t ≈ tc ; they reported the appearance of a CE AFI second phase having a volume fraction that increased with pressure below TOO = TN . Since pressure

Fig. 62. Thermal conductivities κ(T ) for Pr0.5 (Ca1−x Srx )0.5 MnO3 , x = 0.10, 0.15, 0.20. The electronic component κ e for the most conductive sample (x = 0.20) is also shown, after Rivadulla et al. (2002).

Fig. 63. Magnetization M(T ) in H = 10 Oe after ZFC and FC in 10 Oe (closed circles); thermoelectric power α(T ) (open circles) for Pr0.5 (Ca0.75 Sr0.25 )0.5 MnO3 (t = 0.976), after Rivadulla et al. (2002).

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Fig. 64. Thermoelectric power α(T ) and magnetization M(T ) in H = 1 T after ZFC and FC for Pr0.5 (Ca0.5 Sr0.5 )0.5 MnO3 (t = 0.980) (open squares) and Pr0.5 (Ca0.25 Sr0.75 )0.5 MnO3 (t = 0.985) (open circles), after Rivadulla et al. (2002).

increases t and suppresses phase II, pressure stabilizes phase III in the two-phase domain FMV + III. Figure 63 shows α(T ) and both ZFC and FC M(T ) in 10 Oe for a t = 0.976 crystal lying in the two-phase region between phases II and III. This ﬁgure is to be compared with ﬁgs. 58 and 60. A TC ≈ 230 K for the FMV matrix is only a little higher than the TCO of the minority phase; below TCO , the volume fraction of the CO phase competes with that of the FM phase and appears to become dominant in the interval Tp < T < TOO = TN of that phase. Finally, ﬁg. 64 shows M(T ) in H = 1 T and α(T ) curves for samples Pr0.5(Ca0.5 Sr0.5 )0.5 MnO3 (t = 0.980) and Pr0.5 (Ca0.25 Sr0.75)0.5 MnO3 (t ≈ 0.9846). The former has a majority phase III with a minority phase IV; a sharp increase in |α(T )| occurs between Tp and TOO = TN . The latter is primarily phase IV with a small volume fraction of phase III. The apparent suppression of M(T ) in the t = 0.980 sample is due to the smaller temperature interval TOO = TN < T < TC .

4. Conclusions The rare-earth ions in the R1−x Ax MnO3 perovskites have their primary inﬂuence on physical properties through the geometric tolerance factor t that determines the bending of the (180◦ − φ) Mn–O–Mn bond angle to achieve matching of the equilibrium A–O and Mn–O bond lengths. The variance σ 2 of the A-site-cation size plays an important, but secondary role. In this family, the tolerance factor can be varied so as to change the character of

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the σ -bonding electrons of e-orbital parentage at high-spin Mn(III) ions from localized to itinerant behavior while the π -bonding t 3 conﬁgurations remain localized with a spin S = 3/2. The twofold orbital degeneracy of the e electrons at octahedral-site Mn(III) induces local Jahn–Teller site distortions that may locally ﬂuctuate cooperatively or order into a longrange, cooperative static deformation of the lattice. The orbital degeneracy may also be removed where the σ -bonding electrons are itinerant. Whereas itinerant electrons of e-orbital parentage would normally occupy 3D σ ∗ bands, orbital ordering may constrain these electrons (1) to 2D x 2 − y 2 σ ∗ bands or (2) to 1D (3z2 − r 2 )σ ∗ bands that tend to form chargedensity waves, or (3) to two-Mn Mn3.5+ –O–Mn3.5+ Zener polarons. Electrons in 3D σ ∗ bands couple the localized S = 3/2 spins ferromagnetically via de Gennes double exchange. Constraining the itinerant electrons to 2D planes or 1D chains allows de Gennes ferromagnetic double-exchange coupling only in the metallic planes or chains; perpendicular superexchange interactions couple the ferromagnetic units antiferromagnetically. Ferromagnetic double-exchange coupling within a Zener polaron may result in superparamagnetic clusters where the polarons are disordered in a paramagnetic phase, and ordering of the Zener polarons into linear or zig-zag chains gives ferromagnetic superexchange interactions between polarons of a chain, but antiferromagnetic superexchange interactions perpendicular to the chains. Where the e electrons are localized, orbital ﬂuctuations introduce vibronic ferromagnetic Mn(III)–O–Mn(III) and Mn(III)–O–Mn(IV) interactions, but long-range cooperative orbital ordering constrains the ferromagnetic interactions to planes or chains with antiferromagnetic superexchange interactions between the ferromagnetic elements. Moreover, localized electrons in mixed-valent MnO3 arrays experience strong coulomb interactions that give short-range charge-order ﬂuctuations or long-range charge ordering. Optimization of the exchange and coulomb forces produces long-range charge and orbital ordering at lower temperatures. The crossover from localized to itinerant electronic behavior is ﬁrst-order, and the consequent double-well potential for the equilibrium Mn–O bond length can be accommodated in the perovskite structure by cooperative oxygen displacements perpendicular and/or along a Mn–O–Mn bond axis. Cooperative bond-length ﬂuctuations permit the coexistence of competing phases in what appears to a diffraction experiment to be a single phase. Where an external input stabilizes one competing phase relative to another, the bond-length ﬂuctuations allow one phase to grow at the expense of another at lower temperatures. Bond-length ﬂuctuations may also suppress long-range order altogether to give quantum critical behavior at a QCP. In addition, bond-length ﬂuctuations are associated with disorder of a cooperative Jahn–Teller distortion, and these ﬂuctuations can allow partial, ﬂuctuating disproportionation of 2Mn(III) into Mn(IV) and Mn(II). The result of all these competitions is a rich array of physical phenomena to be explored and exploited. An appropriate choice of rare-earth and alkaline-earth A-site cations can change physical properties dramatically and allow the design of materials with unusual physical properties that may prove technologically useful.

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Handbook on the Physics and Chemistry of Rare Earths Vol. 33 edited by K.A. Gschneidner, Jr., J.-C.G. Bünzli and V.K. Pecharsky © 2003 Elsevier Science B.V. All rights reserved

Chapter 215 PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS FOR EXTRACTING SOLUTION STRUCTURES Claude PIGUET Department of Inorganic, Analytical and Applied Chemistry, University of Geneva, 30 quai E. Ansermet, CH-1211 Geneva 4, Switzerland E-mail: [email protected] Carlos F.G.C. GERALDES Department of Biochemistry, Faculty of Science and Technology, and Centre of Neurosciences, University of Coimbra, 3000 Coimbra, Portugal E-mail: [email protected]

Contents List of symbols 1. Introduction 2. Theory 2.1. Nuclear relaxation in paramagnetic lanthanide complexes for extracting R-nucleus distances 2.1.1. Lanthanide-induced contact relaxation 2.1.2. Lanthanide-induced dipolar relaxation 2.1.3. Lanthanide-induced Curie-spin relaxation 2.2. Contact shifts and through-bond spin delocalisation in paramagnetic lanthanide complexes 2.3. Pseudo-contact shifts and through-space interactions in paramagnetic lanthanide complexes 2.3.1. Origin and modeling of magnetic anisotropy in paramagnetic lanthanide complexes 2.4. Separation of contact and pseudo-contact contributions in paramagnetic lanthanide complexes

354 355 358

358 359 361 362

364

366

368

372

2.4.1. Calculation of the anisotropic part of the magnetic susceptibility tensor with structural models 2.4.2. The model-free methods 2.4.2.1. Reilley’s method 2.4.2.2. Crystal-ﬁeld independent methods 2.4.2.3. The special case of rhombic systems 3. Application of the model-free methods to axial monometallic lanthanide complexes with sterically rigid ligands 3.1. Complexes with threefold symmetry 3.1.1. [R(L1 –2H)3 ]3− (L1 = oxydiacetic acid) 3.1.2. [R(L2 )3 ]3+ (L2 = 2,6-bis(benzimidazole)pyridine) 3.1.3. [R(L3 )3 ]3+ (L3 = 2,6-pyridinedicarboxylic acid-bis-diethylamide) 3.1.4. [R(L4 )]3+ and [R(L4 +H)]4+ (L4 = tris{2-[N -methylcarbamoyl(6-(N ,N -diethylcarbamoyl)pyridine-2)ethyl]amine}) 353

373 376 376 377 379

380 381 381 384 387

390

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C. PIGUET AND C.F.G.C. GERALDES

3.1.5. [RM(L5 )3 ]5/6+ (M = Zn, Co; L5 = 2-{6-[N ,N -diethylcarboxamido]-pyridin-2-yl}-1,1’-dimethyl-5,5’-methylene-2’-(5-methylpyridin-2-yl)bis(1H-benzimidazole) 3.1.6. [R(L6 )]3+ (L6 = azacryptand, see ﬁg. 26) 3.1.7. [R(L7 –2H)3 ]3− (L7 = 2,6-pyridinedicarboxylic acid and derivatives) 3.1.8. [R(L8 –3H)] (L8 = 1,4,7-triazacyclononane-N ,N ’,N ”-triacetic acid) 3.2. Complexes with fourfold symmetry 3.2.1. [R(L9 –H)4 ]− (L9 = dithiomethylphosphinic acid and dithiophosphorus acid and dithiophosphorus acid derivatives) 3.2.2. [R(L10 –4H)]− (L10 = 1,4,7,10tetraazacyclododecane-N ,N ’,N ”, N ”’-tetraacetic acid) 3.2.3. [R(L11 )]3+ (L11 = 1,4,7,10tetraazacyclododecane-1,4,7,10tetrakis(N ,N -diethylacetamide)) 3.2.4. [R(L12 –8H)]5− (L12 = 1,4,7,10tetraazacyclododecane-1,4,7,10tetrakis(methylenephosphonic acid))

393 401

404 410 415

415

419

426

430

3.2.5. Comparison of the structures of the [R(L10 –4H)]− , [R(L11 )]3+ and [R(L12 –8H)]5− complexes 3.2.6. [R(L13 –2H)2 ]− (L13 = phtalocyanine) 4. Application of the model-free methods to axial bimetallic lanthanide complexes with sterically rigid ligands 4.1. Complexes with threefold symmetry 4.1.1. [R 2 (L14 –2H)3 ] (L14 = bis{1ethyl-2-[6’-carboxy)pyridin-2’-yl] benzimidazol-5-yl}methane) 4.2. Complexes with fourfold symmetry 4.2.1. [R 2 (L15 –2H)3 ] (L15 = octaethylporphyrin) 5. Application of the model-free methods to axial trimetallic lanthanide complexes with sterically rigid ligands 5.1. Complexes with threefold symmetry 5.1.1. [R 3 (L16 –3H)2 (OH2 )6 ]3+ (L16 = 1,3,5-triamino-1,3,5-tridesoxy-cisinositol) 5.1.2. [R 3 (L17 )3 ]9+ (L17 = 2,6-bis{{1ethyl-2-[6-(N ,N ’-diethylcarbamoyl)-pyridin-2-yl]benzimidazol5-methylene}-(2-ethyl-benzimidazol-5-yl)}pyridine 6. Conclusions References

437 440

443 444

444 448 448

453 454

454

455 459 460

List of symbols Ai

Fermi hyperﬁne constant for a nucleus i

Sz

expectation value of Sz

Bqk Cqk

crystal-ﬁeld parameters of rank k spherical tensor operators of rank k

T1 T2

longitudinal nuclear relaxation time transversal nuclear relaxation time

Cj

Bleaney’s factor of lanthanide j (scaled to −100

Tr(χ )

trace of the magnetic susceptibility tensor

Fi

for Dy(III)) contact term of the nucleus i

β χ

Bohr magneton magnetic susceptibility tensor

ge Gi

Landé factor axial geometrical factor of the nucleus i

χ0

isotropic part of the magnetic susceptibility tensor

χαβ

αβ component of the magnetic susceptibility

δjbulk

tensor bulk paramagnetic shift induced by a lanthanide

Hi

rhombic geometrical factor of the nucleus i

H0 J

applied magnetic ﬁeld total angular momentum quantum number

Jz

expectation value of Jz

k NA

Boltzmann constant Avogadro’s number

δij

hyperﬁne chemical shift for a nucleus i in a complex of a lanthanide j

ri S

R-nucleus i distance spin quantum number

δidia

diamagnetic shift in ppm for a nucleus i

j exp

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS para

355

δij

paramagnetic hyperﬁne chemical shift in ppm

φi

spherical coordinate of nucleus i

c δij

for a nucleus i in a complex of a lanthanide j paramagnetic contact shift in ppm for a nucleus

μeff θi

effective electronic magnetic momentum in μB spherical coordinate of nucleus i

i in a complex of a lanthanide j paramagnetic pseudo-contact shift in ppm for a

τc τe

characteristic correlation time electron spin relaxation characteristic time

nucleus i in a complex of a lanthanide j

τr

rotational characteristic time

ECF crystal-ﬁeld splitting of the ground J multiplet in cm−1

τm ω

chemical exchange characteristic time Larmor precession frequency in Hz

ζ

spin orbit coupling constant

pc

δij

γ

magnetogyric ratio

1. Introduction Intense research activities during the last decade have demonstrated that a judicious combination of dative bonds (i.e., coordination bonds) with non-covalent interactions (i.e., electrostatic, hydrogen bonds, hydrophobic forces, etc.) provides well-deﬁned and structurally rigid metal-containing architectures in which the geometrical and electronic structures can be ﬁnely tuned (Piguet et al., 1997; Lehn, 2000; Steed and Atwood, 2000; Swiegers and Malefetse, 2000; Holliday and Mirkin, 2001). Planned chemical, mechanical and electronic functions may be further implemented to produce supramolecular devices and machines (Piguet and Bünzli, 1998; Kahn, 2000; Balzani et al., 2000). The pronounced stereoelectronic preferences of d-block transition metal ions associated with their peculiar dn electronic conﬁgurations have been systematically exploited to control the ﬁnal molecular or supramolecular architectures according to the Lock and Key concept (Leininger et al., 2000; Fujita et al., 2001). The versatile coordination properties of 4f-block ions (i.e., the lanthanides R(III)) often prevent their use as templating agents in sophisticated molecular or supramolecular assemblies and the structural programming of the metallic sites remains challenging. On the other hand, the Induced ﬁt concept takes advantage of speciﬁc non-covalent interstrand interactions to control the size, the shape and the geometry of the metallic site, thus leading to discrete lanthanide-containing ediﬁces in which a rational design of the associated functions relies on the chemist’s capacity (i) to impose speciﬁc metallic environments and supramolecular structures and (ii) to extract reliable electronic and geometric informations in order to iteratively improve molecular programming (Piguet and Bünzli, 1999; Fu and Turro, 1999; Bruce et al., 2000; Parker, 2000; Piguet et al., 2000; Zhang et al., 2001; Bünzli and Piguet, 2002). The latter point is crucial because minute structural variations may induce (i) drastic size-discriminating effects along the lanthanide series (Petoud et al., 1997), (ii) new optical properties (Gamelin and Güdel, 2000) and huge magnetic anisotropies (Mironov et al., 2001). The characterisation of solid state structures of intermediate sizes has beneﬁted from the recent development of array detectors and the crystallization processes leading to large semi-rigid supramolecular ediﬁces remains the limiting factor for extracting reliable geometrical informations in this context. However, considerable structural changes

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may occur between solid-state and solution (solvation, relaxation of packing constraints, dissociation, etc.) and it is crucial to extract reliable structural and electronic data in solution if self-assembly processes are to be improved. As a result of their peculiar inner-shell 4f n electronic conﬁgurations, the lanthanides display electrostatic metal–ligand bonds with minor covalency and unpaired spin delocalisation is very limited. R(III) (R = Ce–Yb) can be thus considered as paramagnetic dots which affect the magnetic properties of the molecular or supramolecular ediﬁces in a predictable way. For a synthetic chemist, paramagnetism is often considered as a severe handicap for interpreting NMR spectra because (i) the bulk magnetic susceptibility translates the NMR spectrum by a constant (Löliger and Scheffold, 1972), (ii) the NMR signals are severely broadened by the increased nuclear relaxation induced by the electronic magnetic momentum and (iii) the hyperﬁne chemical shift of each proton i drastically depends on its topological and geometrical location with respect to the paramagnetic centre (Bertini and Luchinat, 1996). However, detailed structural and electronic informations can be gained from paramagnetic contributions to the NMR data if an adequate modeling of the magnetic properties is available. Firstly, Evans (1959) and Evans et al. (1971) have established that the bulk paramagnetic susceptibility for a complex of a lanthanide j affects the chemical shifts of all nuclei by a constant value δjbulk (in ppm) which is given by eq. (1) δjbulk

=

μeff 2.828

2 ·

sf · c · 103, T

(1)

μeff is the effective electronic magnetic momentum (in Bohr magnetons), T is the absolute temperature (in K), c is the molar concentration of the paramagnetic lanthanide complex (in mol · dm−3 ) and sf is the shape factor of the magnet (sf = 4π/3 for a cylindrical sample in a superconducting magnet (Baker et al., 1988)) and 2.828 = 3k/(NA β 2 ). This term vanishes when a frequency-locked spectrometer is used together with an internal standard as a reference for chemical shifts, two conditions which are usually met when recording NMR spectra (Peters et al., 1996). However, δjbulk can be of interest for the determination of effective electronic magnetic momenta (μeff ) and associated isotropic paramagnetic susceptibilities (χ0 = (1/3) Tr(χ), eq. (2)) of lanthanide complexes in solution after corrections for solvent effects (Grant, 1995) and diamagnetic contributions (Piguet, 1997). Recently, the measurement of δjbulk induced by paramagnetic lanthanide MRI contrast agents has been used for addressing their in vivo concentrations (Corsi et al., 2001). μeff = 2.828 χ0 · T . (2) Secondly, the lanthanide induced relaxation (LIR) responsible for the broadening of the NMR signals (i.e., the decrease of characteristic longitudinal (T1 ) and transversal (T2 ) nuclear relaxation times) can be traced back to ﬂuctuations of the magnetic ﬁeld induced by variations of the electronic magnetic momenta due to electronic relaxation, molecular tumbling and chemical exchange processes. Theoretical background has been given by Solomon (1955) and Bloembergen and Morgan (1961), and the recent developments of slow-relaxing Gd(III) complexes working as contrast agents for magnetic resonance

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

357

imaging (MRI) have contributed to improve theoretical modeling (Peters et al., 1996; Aime et al., 1998; Babailov and Krieger, 1998; Caravan et al., 1999; Geraldes, 1999; Sharp, 2001). As far as the elucidation of molecular structures of lanthanide complexes in solution is concerned, fast-relaxing paramagnetic ions (R = Ce–Yb, except Gd) are better candidates for extracting lanthanide-nucleus i distances from the electronic-induced paramagnetic dipolar and spin-Curie contributions to the nuclear relaxation processes (Bertini et al., 1993a; Aime et al., 1992a). A short description of this technique together with relevant applications for exploring the solution structures of axial lanthanide complexes is proposed in the next section, although the relaxation processes are not the central theme of this review. Fipara nally, the hyperﬁne paramagnetic lanthanide induced shift (LIS, δij ) contains crucial informations about (i) electronic structures and spin delocalisation (via the contact contribution δijc ) and (ii) molecular structures and magnetic anisotropies (via the pseudo-contact conpc tribution δij ) (Sherry and Geraldes, 1989; Bertini and Luchinat, 1996; Peters et al., 1996; Forsberg, 1996). The experimental hyperﬁne shift of a nucleus i in a paramagnetic complex exp of a lanthanide j (δij in ppm) can be partitioned according to eq. (3) in which δidia corresponds to the underlying diamagnetic shift measured for the analogous 4f0 (R = La, Y) or 4f14 conﬁgurations (R = Lu) and δjbulk is the bulk paramagnetic susceptibility (δjbulk = 0 when an internal reference is used) exp

para

δij = δidia + δjbulk + δij

pc

= δidia + δjbulk + δijc + δij .

(3a)

para

The hyperﬁne paramagnetic contribution (LIS, δij ) corresponding to the sum of contact (through-bond) and pseudo-contact (through-space) effects is easily obtained from the experimental NMR data: para

LIS = δij

pc

exp

= δijc + δij = δij − δidia .

(3b)

Since the ﬁrst observations by Hinckley (1969) demonstrating the ability of lanthanide chelates to induce paramagnetic LIS shifts, theoretical modeling has established the physical origins of the contact (Golding and Halton, 1972; Pinkerton et al., 1985) and pseudo-contact (Bleaney, 1972; Bleaney et al., 1972; Golding and Pyykkö, 1973; Stout and Gutowsky, 1976; Horrocks, 1977; McGarvey, 1979) contributions. Interestingly, for a given paramagnetic lanthanide, δijc depends exclusively on the magnitude of the spin delocalisation mediated by scalar Fermi interactions, and thus reﬂects the topology and the nature of the chemical bonds separating the paramagnetic lanthanide and the nucleus under investigation. On the other pc hand, δij results from the residual isotropic dipolar coupling between the electronic and nuclear magnetic momenta which depends on the molecular magnetic anisotropy induced by the lanthanide and the geometrical position of the nucleus under investigation. This second term contains the geometrical informations required to extract molecular structures in solution and much efforts have been focused on reliable and physically-meaningful separations of these two contributions from the experimental LIS (Reilley et al., 1975, 1976; Desreux and Reilley, 1976; Kemple et al., 1988; Forsberg et al., 1995; Lisowski et al., 1995a). Once reliable pseudopc contact terms are at hand, the complicated dependence of δij on the internal coordinates and

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on the anisotropic part of the magnetic susceptibility tensor (see sect. 2.3) requires some preliminar assumptions. If (i) a large number of reliable pseudo-contact shifts are accessible and (ii) an efﬁcient modeling of the three-dimensional structure is accessible (as in proteins), the calculation of the magnetic susceptibility tensors from an initial structural model followed by iterative non-linear least-squares ﬁts provides the desired structural and magnetic informations (structure-dependent method: Kemple et al. (1988), Forsberg et al. (1995), Lisowski et al. (1995a)). For lanthanide complexes of intermediate size, contact contributions are rarely negligible and it is necessary to use a reliable a priori model of the magnetic anisotropy produced by the lanthanide site in order to extract the missing structural informations (modelfree method, Bleaney (1972)). Both approaches have been addressed in two recent reviews by Forsberg (1996) and Peters et al. (1996) who conclude that structure-dependent techniques are better suited for solving solution structures since the magnetic anisotropy is obtained as a ﬁtted parameter. However, the difﬁcult structural and geometrical modeling of semi-rigid supramolecular ediﬁces of intermediate size containing numerous weak noncovalent interactions and dative bonds (Fraternali and Wipff, 1997; Ulrich et al., 1997; Berny et al., 1999) combined with the extreme sensitivity of programmed functions to minor structural changes in lanthanide complexes have led to a revival of the model-free techniques for detecting crystal-ﬁeld variations and structural changes (Ren and Sherry, 1996; Platas et al., 1999; Rigault et al., 2000a, 2000b). Since the seminal reviews of Forsberg (1996) and Peters et al. (1996), the application of the classical structure-independent one-nucleus method for axial lanthanide complexes has shown some limitations (Rigault and Piguet, 2000) and further developments including two- and three-nuclei techniques (Platas et al., 1999; Geraldes et al., 2001) based on original concepts previously introduced by Reuben (1982) and Spiliadis and Pinkerton (1982) have been implemented for establishing isostructurality and electronic structures (Ren and Sherry, 1996; Platas et al., 1999; Rigault et al., 2000a, 2000b). This review focuses on the use and limitations of the model-free methods in axial paramagnetic supramolecular mono- and polymetallic lanthanide-containing complexes. A comprehensive survey of the systems with three- and fourfold symmetry for which these techniques have been applied is proposed together with a detailed discussion of the limitations of Bleaney’s approach for the modeling of paramagnetic anisotropies and the detection of structural changes along the lanthanide series.

2. Theory 2.1. Nuclear relaxation in paramagnetic lanthanide complexes for extracting R-nucleus distances For any nucleus i of a paramagnetic lanthanide complex in the absence of signiﬁcant chemical exp exp exchange, the experimental longitudinal (1/T1i ) and transversal (1/T2i ) nuclear relaxation dia rates are given by eqs. (4), (5) in which Ti corresponds to the characteristic relaxation times para are of the same nucleus i in the analogous diamagnetic complex (R = La, Y, Lu) and Ti

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

359

the paramagnetic contributions induced by the lanthanide metal ion (Peters et al., 1996), 1 exp T1i

=

1 T1idia

+

1

(4)

para , T1i

1 1 1 exp = dia + para . T2i T2i T2i

(5) para

The paramagnetic contributions 1/Ti , often termed as lanthanide-induced relaxation (LIR), arise from inner-sphere and outer-sphere mechanisms, the latter being negligible for molecular or supramolecular complexes in which the nuclei under investigation are embedded into bulky and semi-rigid organic ligand strands exhibiting slow chemical exchange (Peters et al., 1996; Platas et al., 1999). The paramagnetic inner-sphere relaxation may be traced back to the ﬂuctuating magnetic ﬁeld produced by the electronic magnetic momentum which induces nuclear spin transitions for nuclei whose magnetic momentum interacts with the electronic magnetic momentum (Solomon, 1955; Bloembergen and Morgan, 1961; Bertini and Luchinat, 1996; Peters et al., 1996). This electron–nucleus interaction is randomly modulated by a characteristic correlation time τc which depends on the electron spin relaxation (τe , Sharp et al. (2001)), molecular tumbling (τr ) and chemical exchange (τm ). Since only the rate constants are additive, τc is given by eq. (6), and it is dominated by the shortest correlation time, τc being even smaller than this one (Clementi and Luchinat, 1998) 1 1 1 1 = + + . τc τe τr τm

(6)

For semi-rigid molecular and supramolecular complexes considered in this review, the nuclei under investigation only exhibit slow chemical exchange and τm does not signiﬁcantly contribute to τc (τm τe , τr ). It will not be considered further in the discussion. The interaction between the electronic and nuclear magnetic momenta has two physical origins: contact (through-bond) and dipolar (through-space) effects, but three different mechanisms (one for contact and two for dipolar effects) are responsible for the increase of both the longitudinal (i.e., the decay of the z-component of the nuclear magnetisation) and the transversal nuclear relaxation rates (i.e., the loss of coherence of nuclear magnetisation in the xy-plane controlexp 1/2 ling the line width of the NMR signals Δν = 1/(πT2i )). 2.1.1. Lanthanide-induced contact relaxation Unpaired electronic density can be delocalized onto the various nuclei of the complex via through-bond scalar hyperﬁne interactions involving occupied orbitals containing s-character (direct interaction or polarization according to the Fermi mechanism, Wertz and Bolton (1986)). Random electron relaxation thus produces a ﬂip–ﬂop mechanism which affects the nuclear spin and increases nuclear relaxation processes (Bertini and Luchinat, 1996). Since these interactions are isotropic, they do not depend on molecular tumbling and τe is the only relevant correlation time for non-exchanging semi-rigid complexes. Moreover, only electronic spin can be delocalized via hyperﬁne interactions (no orbital contribution) and the contact re-

360

C. PIGUET AND C.F.G.C. GERALDES

laxations given by eqs. (7), (8) involve the spin quantum number S (Bloembergen, 1957). 1 para-contact

T1i

1 para-contact T2i

S(S + 1) Ai 2 2τe , 3 h¯ 1 + ωS2 τe2 S(S + 1) Ai 2 τe τe + , = h¯ 3 1 + ωS2 τe2 =

(7)

(8)

Ai is the Fermi hyperﬁne constant (in Hz) and ωS is the Larmor precession frequency of the unpaired electrons (in Hz). As a result of the very limited covalency of the lanthanide–ligand bonds, Ai are small and only nuclei close to the metallic centre are signiﬁcantly affected. Along the lanthanide series, R(III) = Gd(III) (S = 7/2 and τe ≈ 10−8 –10−9 s, tables 1, 2) is the unique metal ion for which spin momenta (S) and electronic relaxation time (τe ) are large enough to produce signiﬁcant contact contributions. Since ωS2 τe2 is extremely large for para-contact Gd(III) complexes, the contact contribution to the longitudinal relaxation (1/T1i ) is negligible, but the existence of a non-dispersive term for the transverse contact contribution (eq. (8)) implies that this mechanism may dominate the transverse relaxation of water molecules bound to MRI contrasts agents (Aime et al., 1998, 1999a; Caravan et al., 1999). For the other lanthanides (R = Ce–Yb except Gd), the fast electronic relaxation (τe ≈ 10−13 s, table 2) strongly limits contact contributions which can be neglected for the modeling of nuclear relaxation processes in theses complexes.

Table 1 Electronic characteristics of R(III) free ions Conﬁg.

Ions

Ground state

gJ a

μeff /B.M.

ζb /cm−1

1st excited state

4f 1 4f 2 4f 3 4f 4 4f 5 4f 6 4f 7 4f 8 4f 9 4f 10 4f 11 4f 12 4f 13

Ce3+ Pr3+ Nd3+ Pm3+ Sm3+ Eu3+ Gd3+ Tb3+ Dy3+ Ho3+ Er3+ Tm3+ Yb3+

2F

6/7 4/5 8/11 3/5 2/7 5 2 3/2 4/3 5/4 6/5 7/6 8/7

2.54 3.58 3.62 2.68 0.85 0 7.94 9.72 10.65 10.61 9.58 7.56 4.54

737 879 1030 1190 1361 1436 1755 1965 2189 2436 2700 2817 3288

2F

5/2 3H 4 4I 9/2 5I 4 6H 5/2 7F 0 8S 7/2 7F 6 6H 15/2 5I 8 4I 15/2 3H 6 2F 7/2

7/2 3H 5 4L 11/2 5I 5 6H 7/2 7F 1 6P 7/2 7F 5 6H 13/2 5I 7 4I 13/2 3H 5 2F 5/2

Energy state separation /cm−1 2200 2100 1900 1600 1000 300 30000 2000 3300 5300 6500 5700 10000

a g = 1 + J (J +1)+S(S+1)−L(L+1) . The latter formula is not valid for J = 0 and the mathematical limit g = 5 is J J 2J (J +1) given for Eu(III) in its ground state 7 F0 (Kahn, 1993). b Taken from Golding and Halton (1972).

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

361

Table 2 Electronic (τe ) and rotational (τr ) correlation relaxation times for R(III) aqua-complexes Conﬁg.

Ions

4f 1 4f 2 4f 3 4f 4 4f 5 4f 6 4f 7 4f 8 4f 9 4f 10 4f 11 4f 12 4f 13

Ce3+ Pr3+ Nd3+ Pm3+ Sm3+ Eu3+ Gd3+ Tb3+ Dy3+ Ho3+ Er3+ Tm3+ Yb3+

τe (10−12 s, 312 K)a 0.09 0.057 0.115 – 0.045 0.009 – 0.203 0.299 0.194 0.238 0.369 0.137

τe (10−12 s, 298 K)b – 0.082 – – 0.079 – 103 –104 c – 0.39 0.27 0.31 – 0.22

τr (10−12 s, 298 K)b – 63 – – 67 – 41d – 63 65 61 – 68

a Taken from Alsaadi et al. (1980c, 1980d). b Taken from Bertini et al. (1993a). c Taken from Bertini et al. (1993b). d Taken from Powell et al. (1996).

2.1.2. Lanthanide-induced dipolar relaxation According to the classic description of the through-space coupling between two point dipoles, the nuclear and electronic magnetic momenta produce a dipolar interaction which depends on their separation and orientation (Bertini and Luchinat, 1996). Since the electronic magnetic momentum is 2–3 orders of magnitude larger than the nuclear momenta, the interest is restricted to the ﬂuctuation of the magnetic ﬁeld provided by the unpaired electron spins which can induce nuclear transitions via dipolar coupling. The modulation of this interaction results from electronic relaxation (τe ) and molecular tumbling (τr ) leading to the correlation time τc−1 = τe−1 +τr−1 in the absence of chemical exchange. The Solomon equations (eqs. (9), (10)) model this dipolar contribution assuming that the nuclear Larmor procession frequency (ωI ) is negligible with respect to the electronic Larmor frequency (ωS ωI ) (Solomon, 1955; Bertini and Luchinat, 1996) 1 2 μ0 2 γI μ2eff β 2 7τc 3τc (9) , = + para-dipolar 15 4π 1 + ωI2 τc2 1 + ωS2 τc2 ri6 T1i 1 1 μ0 2 γI μ2eff β 2 3τc 13τc 4τc + , (10) = + para-dipolar 15 4π 1 + ωI2 τc2 1 + ωS2 τc2 ri6 T2i μ0 /4π is the magnetic permeability of vacuum, γI is the nuclear magnetogyric ratio, β is the Bohr magneton and ri is the R(III)-nucleus i distance. For molecular and supramolecular complexes of intermediate size discussed in this review, τr ≈ 10−11 –10−9 s (Aime et al., 1992a; Caravan et al., 1999; Rigault et al., 2000b) and τe τr for all lanthanide com-

362

C. PIGUET AND C.F.G.C. GERALDES

plexes except those with R = Gd. However, the electron-nuclear spin coupling is so effective for Gd(III) complexes that high-resolution NMR spectra cannot be recorded as a result of the considerable dipolar paramagnetic contribution to the nuclear relaxation processes. This lanthanide is thus never used for the analysis of hyperﬁne shift data (LIS) discussed in this review and its peculiar effect on relaxation processes will not be further considered here. Detailed and comprehensive treatments of relaxation processes in Gd(III) complexes can be found in excellent recent reviews by Peters et al. (1996), Aime et al. (1998) and Caravan et al. (1999). For R = Ce–Yb (except R = Gd), the modulation of the dipolar electron-nuclear interaction by molecular tumbling is thus negligible and τc ∼ = τe . Finally, τe is usually so short for fast-relaxing R(III) that ωI2 τc2 1 and ωS2 τc2 1 (low-ﬁeld or fast-motion limit, Bertini and Luchinat (1996)) and eqs. (9), (10) simplify to eq. (11) 1 1 4 μ0 2 γI μ2eff β 2 (11) = = τe . para-dipolar para-dipolar 3 4π ri6 T1i T2i This equation justiﬁes the qualitative statement that the shorter the electronic relaxation times, the smaller paramagnetic effects on nuclear relaxation. It also predicts that the dipolar contribution is maximum for strongly paramagnetic lanthanides (via μeff ) and for nuclei located close to the metal ion (via ri ). 2.1.3. Lanthanide-induced Curie-spin relaxation In deriving the contact and dipolar contributions induced by the unpaired electrons (eqs. (7)– (11)), the small difference in the population of the electron spin levels according to the Boltzmann distribution has been neglected (Bertini and Luchinat, 1996). However, this difference accounts for the existence of a time-average magnetic momentum μ. The time-average excess of spin along the quantization z-axis Sz is called the expectation value of the Sz operator and is given by eq. (12) (Bertini and Luchinat, 1996; Bertini et al., 2002) S ge βH0 S(S + 1) MS =−S S, Ms |Sz |S, Ms exp(−ge βH0 MS /kT ) Sz = (12) , =− S 3kT M =−S exp(−ge βH0 MS /kT ) S

ge is the Landé factor and H0 is the applied magnetic ﬁeld responsible for the removing of the degeneracy of the MS spin levels. For lanthanide complexes, Sz must be replaced by Jz because of the considerable orbital contribution to the total angular momentum. The associated static electronic magnetic momentum is given by μ = −ge βSz and it interacts with the nuclear spins via dipolar mechanism. Random modulation of this interaction through molecular tumbling (τr ) may induce nuclear spin transitions and contributes to nuclear relaxation. This second dipolar mechanism described by eqs. (13), (14) is termed Curie-spin relaxation in order to reﬂect its relationship with the static magnetic susceptibility given by the Curie law 1 6 μ0 2 γI2 μ4eff β 4 H02 τr (13) , = para-Curie 5 4π 1 + ωI2 τr2 ri6 (3kT )2 T1i 1 μ0 2 γI2 μ4eff β 4 H02 3τr 1 4τr + . = (14) para-Curie 5 4π ri6 (3kT )2 1 + ωI2 τr2 T2i

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

363

The mathematical forms of the Curie-spin contributions are similar to those found for transient dipolar contributions (eqs. (9)–(11), dependence on ri−6 ) except that (i) they increase with magnetic ﬁeld (via H02 ) and (ii) they are more sensitive to the nuclear magnetogyric ratio and electronic magnetic momentum. The Curie-spin contribution is often much smaller than the dipolar contribution except for 1 H NMR experiments (large γI ) performed at high magnetic ﬁeld (large H0 ) for bulky (large τr ) and strongly paramagnetic (large μeff ) complexes. However, fast-relaxing lanthanide complexes (i.e., possessing very short τe , R = Ce–Yb, except Gd) of intermediate size considered in this review often fulﬁll these criteria and the Curie contributions (eqs. (13), (14)) become comparable with transient dipolar contributions para to the nuclear relaxation (eq. (11)). The associated total paramagnetic contribution 1/Ti processes (eqs. (4), (5)) in the absence of chemical exchange thus corresponds to the sum of these two dipolar contributions and is given by eqs. (15), (16). 1 para

T1i

1 para T2i

4 μ0 2 γI μ2eff β 2 τe + 3 4π ri6 4 μ0 2 γI μ2eff β 2 = τe + 3 4π ri6 =

6 μ0 2 γI2 μ4eff β 4 H02 τr , 5 4π 1 + ωI2 τr2 ri6 (3kT )2 1 μ0 2 γI2 μ4eff β 4 H02 3τr 4τr + . 5 4π 1 + ωI2 τr2 ri6 (3kT )2

(15)

(16)

When τr is determined by an independent experiment such as dipolar relaxation measurements in analogous diamagnetic complexes (Wasylishen, 1987), the magnetic ﬁeld depenpara is relevant for extracting R-nuclei distances (ri ) at a ﬁxed temperature in dence of 1/Ti para solution. Least-squares ﬁts of 1/T1i vs H02 /(1 + ωI2 τr2 ) (eq. (15), Burns and LaMar (1982)) para or 1/T2i vs H02 (4τr + 3τr /(1 + ωI2 τr2 )) (eq. (16), or vs H02 when ωI2 τr2 1, Allegrozzi et al. (2000)) allow the simultaneous estimation of ri from the slope and τ e from the intercept. A linear combination of eqs. (15) and (16) has been proposed to remove τ e from the ﬁtting process thus leading to the determination of ri at a single magnetic ﬁeld (eq. (17), Aime et al. para (1992a)), but this technique requires the accurate determination of T2i which is often prevented by unresolved scalar coupling in supramolecular lanthanide complexes (Carr–Purcell– Meiboon–Gill pulse sequence (Meiboom and Gill, 1958) or line-width analysis (Rigault et al., 2000b)). 1 para

T2i

−

1 para

T1i

=

1 μ0 2 γI2 μ4eff β 4 H02 3τr 4τ . + r 5 4π 1 + ωI2 τr2 ri6 (3kT )2

(17)

When τr is unknown, it can be adjusted together with τe and ri by using non-linear leastsquares ﬁts of eqs. (15), (16) as similarly described for the treatment of NMRD proﬁles (Bertini et al., 1995; Ruloff et al., 1998; Toth et al., 1998), but a much simpler approach considers that both dipolar and Curie-spin contribution depend on ri−6 . When a nucleus for which the R-nucleus distance rref can be estimated either from crystal structure or gas-phase modeling is used as a reference, eq. (15) reduces to its simplest form (eq. (18)) and relative R-nucleus i distances are accessible without estimations of τe and τr (Barry et al., 1971;

364

C. PIGUET AND C.F.G.C. GERALDES

Forsberg, 1996; Brink et al., 1996) para T1i ri 6 = . para rref T1ref

(18)

The latter technique is particularly appreciated by coordination chemists because of its simple mathematical formulation and the limited amount of experimental data to be collected (longitudinal relaxation times at a single magnetic ﬁeld obtained by the inversion–recovery method (Vold et al., 1968)). However, the a priori choice of a reference distance (rref ) requires a partial modeling of the complex and the extracted distances strongly depend on the accuracy of this original choice. 2.2. Contact shifts and through-bond spin delocalisation in paramagnetic lanthanide complexes Since electrons relax orders of magnitude faster than nuclei, the nucleus in each of its MI energy level only senses an average static magnetic momentum μ = −ge βSz which results from the slight excess of electron population in the MS = −1/2 state. In paramagnetic NMR, the nucleus under investigation is rarely that bearing the unpaired electrons. Delocalisation of the spin density occurring either through direct Fermi hyperﬁne interaction or polarization of occupied s-containing molecular orbitals (Wertz and Bolton, 1986; Lisowski et al., 1995b), produces an additional magnetic ﬁeld H generated at the nucleus by the fraction of electron magnetic momentum located at the nucleus itself. Since the nuclear resonance frequency (i.e., the chemical shift) depends on the total magnetic ﬁeld, this mechanism provides a contact contribution to the paramagnetic shift of a nucleus i (δic ) which is given by eq. (19) (Bertini and Luchinat, 1996). δic =

H Ai = Sz . H0 h¯ γI H0

(19)

Substituting the value Sz given by eq. (12) for a pure spin contribution arising from the metallic centre into eq. (19) gives eq. (20) which predicts (i) a T −1 dependence of δic and (ii) large contact shifts for strongly paramagnetic complexes possessing efﬁcient spin delocalisation δic =

Ai ge βS(S + 1) . · 3γI kT h¯

(20)

Strictly speaking, δic is not isotropic when ge varies with molecular orientation (i.e., the magnetic susceptibility tensor is anisotropic), but typical values for proton hyperﬁne anisotropy amounts to ≈ 105 Hz which is much smaller than τr−1 in solution, thus leading to the observation of average isotropic contact shifts (ge should be therefore replaced by g¯ in eq. (20), Bertini and Luchinat (1996)). For lanthanides, the contact contribution is strongly limited by the minute covalency of the metal–ligand bonds and only weak spin delocalisation involves the 6s metal orbital which in turn slightly polarizes the 4f orbitals (Lewis et al., 1962; Lisowski et al., 1995b). Therefore contact contributions only affect nuclei topologically close

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

365

to the lanthanide metal ion and the hyperﬁne constants Ai rapidly decrease with increasing separation (Ai is usually negligible for a R(III)-nucleus separation larger than three bonds). Equation (19) holds for lanthanide complexes because the spin expectation value Sz explicitly considers the populations of the ground and excited J manifold levels together with second-order terms mixing excited states with the ground state (Golding and Halton, 1972). For each J manifold, the expectation value Sz J is given by eq. (21) and a Boltzmann distribution for the populations of the involved levels allows the calculation of Sz (eq. (22), λ = ±ζ /2S in which ζ is the spin orbit coupling constant collected in table 1) βH0 2kT Sz J = − (21) gJ (gJ − 1)J (J + 1) + (gJ − 1)(gJ − 2) , 3kT λ Sz J (2J + 1) exp(−λJ (J + 1)/2kT ) . Sz = J (22) J (2J + 1) exp(−λJ (J + 1)/2kT ) Numerical calculations of Sz at 300 K obtained with eq. (22) for all R(III) free ions are collected in table 3 (Golding and Halton, 1972). Pinkerton et al. (1985) have demonstrated that Sz are relatively insensitive to the choice of various sets of reported spin-orbit coupling constants. Moreover, except for R = Sm and Eu, Sz displays a minor dependence on the temperature and the data calculated at 300 K (table 3) are amenable for a reliable treatment of contact shifts in solution around room temperature. The close proximity of excited states possessing different J manifolds for Sm(III) requires a precise calculation of Sz at each temperature as is the case for R = Eu. However, the latter metal brings some speciﬁc complications associated with the absence of a well-deﬁned gJ value for its J = 0 ground state. Golding Table 3 Spin expectation valuesa Sz and Bleaney’s factorsb C for R(III) free ions at 300 K, and rhombic proportionality factorsc C rhombic Conﬁg.

Ions

Sz

C

C rhombic

4f 1

Ce3+

4f 2 4f 3 4f 4 4f 5 4f 6 4f 7 4f 8 4f 9 4f 10 4f 11 4f 12 4f 13

Pr3+ Nd3+ Pm3+ Sm3+ Eu3+ Gd3+ Tb3+ Dy3+ Ho3+ Er3+ Tm3+ Yb3+

−0.98 −2.97 −4.49 −4.01 0.06 10.68 31.50 31.82 28.55 22.63 15.37 8.21 2.59

−6.3 −11.0 −4.2 2.0 −0.7 4.0 0.0 −86 −100 −39 33 53 22

– −0.6 −2.3 – – 3.4 – 7.7 −55.7 −13.6 −3.8 −34.0 4.7

a Taken from Golding and Halton (1972). b Values relative to C Dy = −100 including mixing with excited states (Bleaney,

1972; Bleaney et al., 1972). c Values relative to C = −100 (Reuben and Elgavish, 1980). Dy

366

C. PIGUET AND C.F.G.C. GERALDES

and Halton (1972) used the mathematical limit gJ = 5 for Eu(7F0 ) (Kahn, 1993) in order to obtain Sz = 10.68 reported in table 3. Pinkerton et al. (1985) proposed gJ =0 = 4.4 from experimental ﬁts of contact contributions, thus leading to Sz = 7.57 at 300 K. This incertitude may limit the determination of hyperﬁne constants for Eu(III) complexes. Interestingly, Sz can be positive or negative for R(III) ions and may considerably differ from the spin-only value owing to the large orbital contributions. On the other hand, the use of Sz , and not Jz , is adequate because only the spin is delocalized onto the molecules (Bertini and Luchinat, 1996). Equations (21), (22) assume that (i) kT > Zeeman splitting and (ii) crystal-ﬁeld effects are negligible (ECF < kT ). The ﬁrst hypothesis is justiﬁed for NMR measurements around room temperature, but the second one is more debatable, particularly for lanthanide complexes with ‘soft’ donor ligands providing large crystal-ﬁeld effects ECF > 400 cm−1 (Mironov et al., 2000). However, the extremely narrow range of μeff observed at room temperature for lanthanide complexes displaying various structures and geometries (Kahn, 1993; Bünzli, 1998; Kaltsoyannis and Scott, 1999) suggest that crystal-ﬁeld splitting has only minor effects on Sz . The recent success of the application of the two-nuclei crystal-ﬁeld independent method (eq. (51)) for the evaluation of isostructurality in rigid axial supramolecular complexes also supports this conclusion (Rigault et al., 2000a, 2000b), but, to the best of our knowledge, a detailed modeling of Sz for speciﬁc crystal-ﬁeld potentials has not been considered in the literature. 2.3. Pseudo-contact shifts and through-space interactions in paramagnetic lanthanide complexes Since the spin delocalisation in lanthanide complexes is small (see sect. 2.1), the unpaired electrons can be considered as spatially conﬁned onto the metal, thus producing an electronic magnetic point dipole which may interact with peripheral nuclear magnetic momenta via dipolar interactions (eq. (23), Bertini and Luchinat (1996)). μ0 1 (μ · r)(μI κ · r)

Edip = − (23) 3 − μ · μ Iκ , 4π r 3 r2 Edip is the energy of the dipolar interaction between the electronic magnetic momentum of the electron (represented by its average value μ) and the nuclear magnetic momentum (represented by its projection along the magnetic ﬁeld μI κ ) and r is the separation between the two magnetic point dipoles. Edip varies for two nuclear spin states differing by MI = ±1 (μI κ depends on the orientation of the nuclear spin vector) which affects the condition of resonance of this nucleus, and thus produces a dipolar contribution δ dip to the chemical shift given by eq. (24), which reduces to eq. (25) for a magnetically isotropic compound Edip (MI ) − Edip(MI +1 ) , h¯ γI H0

1 δ dip = χ 3 cos2 (γ ) − 1 , 3 4πNA ri δ dip =

(24) (25)

χ is the magnetic susceptibility tensor, γ is the angle between the metal-nucleus vector r and the external magnetic ﬁeld. Integration of eq. (25) over all molecular orientations averages

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

367

zero and no dipolar shift is expected for molecules possessing an isotropic magnetic susceptibility tensor (χxx = χyy = χzz ) in solution. However, for an axially anisotropic electronic magnetic momentum (χll = χ⊥ ), eq. (25) becomes eq. (26) and integration over all molecular orientations is no longer zero (Bertini et al., 2002). In the latter equation α is the angle of the z axis with the external ﬁeld direction, θ is the angle between the metal-nucleus vector and the z axis and Ω deﬁnes the position of the metal-nucleus vector on the basal plane of the revolution cone deﬁned by the rotation of the metal-nucleus vector about the z-axis (Bertini and Luchinat, 1996)

δ dip = 4πN1 r 3 χll cos2 α 3 cos2 θ − 1 + χ⊥ sin2 α 3 sin2 θ cos2 Ω − 1 A

+ 34 (χll − χ⊥ ) sin 2α sin 2θ cos Ω . (26) Since this dipolar interaction remains in isotropic media as similarly found for the contact shift (see sect. 2.1), it is often termed as the pseudo-contact shift. For the general case of a complex possessing an anisotropic magnetic susceptibility tensor, Kemple et al. (1988) show pc that the pseudo-contact shift δi of a nucleus i is given by eq. (27) where ri , θi and φi are the spherical coordinates of the resonating nucleus in an arbitrary axes system with the lanthanide metal ion R(III) located at the origin (ﬁg. 1)

pc δi = 1 3 χzz − 13 Tr χ 3 cos2 θi − 1 + (χxx − χyy ) sin2 θi cos 2φi 2NA ri (27) 2

1 + 3 χxy sin θi sin 2φi + χxz (sin 2θi cos φi )χyz (sin 2θi sin φi ) . NA ri

In the principal magnetic axes system, the magnetic susceptibility tensor is diagonal and the three last terms of eq. (27) vanish, thus leading to eq. (28) for the pseudo-contact shifts (Horrocks and Sipe, 1972; Bertini et al., 2002).

pc δi = 1 3 χzz − 13 Tr χ 3 cos2 θi − 1 + (χxx − χyy ) sin2 θi cos 2φi . (28) 2NA ri

Finally, for axial complexes (i.e., complexes possessing a C4 axis), χxx = χyy and eq. (28) reduces to eq. (29) in the principal magnetic axes system (Forsberg, 1996).

pc δi = 1 3 (χzz − χxx ) 3 cos2 θi − 1 . (29) 3NA ri

Fig. 1. Spherical coordinates ri , θi and φi for a nucleus i in an arbitrary xyz reference frame with the lanthanide metal ion R(III) located at the origin.

368

C. PIGUET AND C.F.G.C. GERALDES pc

Equations (27)–(29) imply that pseudo-contact shifts δi are maximum for complexes displaying large molecular magnetic anisotropies and that structural and geometrical informations can be extracted from the so-called non-linear geometrical factors Gi (eq. (30)) and Hi (eq. (31)) (Forsberg, 1996; Peters et al., 1996) Gi = Hi =

3 cos2 θi − 1 ri3

sin2 θi cos 2φi ri3

(30)

, .

(31)

Interestingly, Hawkes et al. (1973) suggested that eq. (29) also holds for stereochemically labile lanthanide complexes exhibiting fast dynamic interconversions in solution, an experimental observation theoretically justiﬁed by Horrocks (1974) for lanthanide shift reagents existing in solution as a set of rapidly interconverting isomers. In a seminal paper, Briggs et al. (1972) demonstrated that the use of the simpliﬁed eq. (29) is justiﬁed for complexes dispc playing fast equilibria between at least three rotamers. In the latter case, δi is proportional to Gi by a factor which is a complicated combination of axial (χzz − (1/3) Tr χ) and rhombic (χxx − χyy ) magnetic anisotropies. The term ‘effective axial symmetry’ is used for describing these complexes. 2.3.1. Origin and modeling of magnetic anisotropy in paramagnetic lanthanide complexes Large paramagnetic anisotropies and associated pseudo-contact shifts are expected when orbital contributions to the ground state is considerable because such contributions are orientation dependent (Bertini and Luchinat, 1996). For lanthanide metal ions, the combination of spin (S) and orbital (L) contributions to the total angular momentum (J ) (modulated via the spin-orbit coupling) produces considerable magnetic anisotropy when crystal-ﬁeld effects due to coordinated ligands remove the spherical symmetry around the metal. The terms of the magnetic susceptibility tensors χαβ can be obtained by using eq. (32) (Gerloch and McMeeking, 1975) which corresponds to the general form of the Van Vleck formula, the latter being deﬁned in the principal magnetic axes system (Kahn, 1993) i|μα |j j |μβ |i NA χαβ = kT i exp(−Ei /kT ) i j i|μα |j j |μβ |i + i|μβ |j j |μα |i exp(−Ei /kT ), − (32) Ei − Ej j

α, β = x, y or z, Ei is the energy of the crystal-ﬁeld state |i produced by the non-spherical arrangement of the donor atoms coordinated to R(III) and μα (α = x, y, z) are the components of the operator of the total magnetic momentum μ. The energies of the wave functions |i of crystal-ﬁeld states in a lanthanide complex are obtained from the diagonalisation of the model Hamiltonian H = H0 + HCF where H0 is the free-ion Hamiltonian and HCF is the crystal-ﬁeld Hamiltonian (Mironov et al., 2001, 2002). The latter is usually written in terms of phenomenological Bqk crystal-ﬁeld parameters and Cqk spherical tensor operators (eq. (33),

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

Görller-Walrand and Binnemans (1996)) Bqk Cqk . HCF =

369

(33)

kq

Mironov et al. (2001, 2002) have followed this approach to compute theoretical magnetic anisotropies 1 3 1 χ = χzz − (χxx + χyy ) = χzz − Tr χ 2 2 3 at 298 K for eight-coordinate (Mironov et al., 2001) and nine-coordinate (Mironov et al., 2002) lanthanide complexes possessing arbitrary (but reasonable) crystal-ﬁeld parameters. Figure 2 shows typical magnetic anisotropies χ calculated for various distortions of an eight-coordinate cubic lanthanide complex. Such exact calculations require accurate structural, geometric and electronic parameters for the R-ligand bonds and for the metallic coordination spheres which are usually not accessible for coordination complexes in solution. Only solid-state structures for which X-ray crystal structures and Bqk parameters have been determined, can be satisfyingly modeled with this approach (Görller-Walrand and Binnemans, 1996; Hopkins et al., 1996, 1998). Moreover, no analytical formula expressing χ as a function of Bqk and metal-centred electronic properties can be introduced into eqs. (27)–(29) for extracting solution structures from NMR pseudocontact shifts. In order to overcome this limitation, Bleaney (1972) has proposed a hightemperature expansion of the magnetic susceptibility tensor given by eq. (32) in a power series in the inverse temperature. The ﬁrst term in T −1 corresponds to the isotropic magnetic susceptibility χ0 = (1/3) Tr χ of the free lanthanide ion (eq. (34)) χ0 =

NA gJ2 β 2 1 Tr χ = J (J + 1). 3 3kT

(34)

The second terms in T −2 (eqs. (35)–(37)) correspond to the anisotropic part of the magnetic susceptibility related to the Cqk operators of rank two (k = 2) associated with crystal ﬁeld parameters A02 r 2 and A22 r 2 (which are related to conventional Bqk parameters by B02 = 2A02 r 2 and B22 = (2/3)1/2 A22 r 2 (Görller-Walrand and Binnemans, 1996)) NA β 2 2 0 r A2 − A22 (1 + p)ξ, 2 30(kT ) NA β 2 2 0 r A2 + A22 (1 + p)ξ, χyy − χ0 = 2 30(kT ) NA β 2 2 0 r 2A2 (1 + p)ξ. χzz − χ0 = − 30(kT )2 χxx − χ0 =

(35) (36) (37)

The quantity ξ is given in eq. (38) where J αJ is a numerical coefﬁcient tabulated by Bleaney (1972) for each 4f n -electronic conﬁguration ξ = gJ2 J αJ J (J + 1)(2J − 1)(2J + 3).

(38)

370

C. PIGUET AND C.F.G.C. GERALDES

Fig. 2. Variations of the computed magnetic anisotropies χ with respect to the distortion of a cube toward (a) elongated and compressed tetragonal prisms, (b) a tetragonal antiprism and (c) a dodecahedron (adapted from Mironov et al. (2001)).

The factor (1 + p) in eqs. (35)–(37) reﬂects the contribution of thermally populated excited multiplets of the lanthanide ion which is small for all lanthanides at 300 K except for Sm(III) and Eu(III). In the latter case, the energy of the ﬁrst excited states are close enough from the ground state to require speciﬁc calculations at each temperature. Combinations of eqs. (35)– (37) allows the calculation of the magnetic anisotropy in eq. (39) which predicts that χ depends only on the B02 crystal-ﬁeld parameter. The sign and the magnitude of the magnetic anisotropies along an isostructural series of lanthanide complexes possessing identical B02 parameter only depend on ξ which is positive for R = Eu, Er, Tm, Yb, negative for Ce, Pr,

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

371

Nd, Tb, Dy and maximum for R = Dy (Bleaney, 1972), NA β 2 2 0 1 3 1 χ = χzz − (χxx + χyy ) = χzz − Tr χ = − r A2 (1 + p)ξ 2 2 3 10(kT )2 =−

NA β 2 2 B (1 + p)ξ. 20(kT )2 0

(39)

If the energy of the crystal-ﬁeld splitting ECF produced by the Bqk parameters is much smaller than the thermal energy (kT ≈ 200 cm−1 at 300 K), all the crystal-ﬁeld levels of the ground state have comparable thermal populations and the T −2 term of the power series is adequate for modeling the magnetic anisotropy (Bleaney, 1972; Mironov et al., 2002). q Substitution of eqs. (35)–(37) into eq. (28) gives eq. (40) in terms of A2 r 2 which can be transformed into eq. (41) with conventional Bq2 parameters 2 β 2 (1 + p)ξ 1 0 2

pc 2 2 2 δi = − (40) A θ − 1 + A θ cos 2φ r 3 cos r sin , i i i 2 2 60(kT )2 ri3 √ 2 2 β 2 (1 + p)ξ 1 2

pc 2 B 3 cos sin θ − 1 + 6B θ cos 2φ δi = − (41) i i i . 0 2 120(kT )2 ri3 The ﬁrst numerical terms C = −β 2 (1 + p)ξ /(120(kT )2 ) are often referred to as Bleaney’s factors and their relative values (scaled to CDy = −100) have been tabulated at 300 K for any 4f n conﬁgurations including excited states contributions (table 3, Bleaney et al. (1972)). Finally, the introduction of the geometrical factors deﬁned by eqs. (30), (31) together with C into eq. (41) gives the classical eq. (42) for the pseudo-contact shifts according to Bleaney’s approach (Forsberg, 1996) √

pc δi = C B02 Gi + 6B22 Hi . (42) However, a systematic survey of the crystal-ﬁeld splitting in lanthanide complexes shows that ECF ≈ 300–400 cm−1 is usual and the high-temperature assumption ECF < kT is not fully satisﬁed. Therefore, Cqk operators of rank four (k = 4) and rank six (k = 6) cannot be neglected (Morrison and Leavitt, 1982; Görller-Walrand and Binnemans, 1996; Mironov et al., 2000). According to Bleaney’s approach, the T −n series does not converge at T −2 and further terms must be considered. Golding and Pyykkö (1973) included rank four and rank six crystal-ﬁeld parameters (Bqk , k = 4, 6) for the speciﬁc calculations of the magnetic susceptibilities in crystal-ﬁeld potentials with D3h and C3v symmetries. They found that corrections to the T −2 term are within 20% for RCl3 compounds. Later, McGarvey (1979) derived the complete forms of the T −3 terms which depend on Bqk , k = 2, 4, 6. Since these equations would occupy almost one complete printed page, the reader is referred to the original publication. Application to RCl3 and R(O3 SOEt)3 shows less than 10% deviation from classical Bleaney’s approach (i.e., a power series limited to T −2 ) and it was concluded that the T −3 term (or higher order terms) can be neglected (Stout and Gutowsky, 1976). However, the crystal-ﬁeld splittings experienced by R(III) in RCl3 or in R(O3 SOEt)3 are among the smallest reported (Görller-Walrand and Binnemans, 1996) and high-temperature Bleaney’s

372

C. PIGUET AND C.F.G.C. GERALDES

hypothesis ECF /kT < 1 is satisﬁed. The recent exact calculations of χ by Mironov et al. (2001, 2002) with eqs. (32), (33) for lanthanide complexes with arbitrary crystal-ﬁeld parameters and geometries show that Bleaney’s approach is insufﬁcient to model cases for which ECF > kT . For instance, the distortion of an eight-coordinate tetragonal prismatic complex toward a tetragonal antiprism does not affect B02 and no variation of χ is expected from eq. (39). The computed changes of χ for R = Dy, Tm and Yb (ﬁg. 2b) are thus clearly beyond Bleaney’s theory (ﬁg. 2b, Mironov et al. (2001)) as is the signiﬁcant deviation of the magnetic anisotropy from the predicted T −2 behaviour noticed by Horrocks (1977) for solid Yb(III) complexes. It can be concluded that Bleaney’s approach is restricted to complexes with small crystal-ﬁeld splitting in a narrow temperature range around 300 K, the reference temperature at which the C factors have been computed (table 3). However, to the best of our knowledge, no systematic investigation of the corrections resulting from T −3 terms has been investigated except for the seminal work of McGarvey (1979). 2.4. Separation of contact and pseudo-contact contributions in paramagnetic lanthanide complexes The substitution of eqs. (19) and (28) into eq. (3) shows that the paramagnetic shift induced by a lanthanide j at a nucleus i is given by eq. (43) para

LIS = δij

pc

= δijc + δij

Ai 1 1 j j χzz − Tr χ 3 cos2 θi − 1 = Sz j + 3 3 h¯ γI H0 2NA ri

j

j + χxx − χyy sin2 θi cos 2φi .

(43)

The use of the deﬁnitions of the geometrical factors Gi (eq. (30)) and Hi (eq. (31)) together with the contact term Fi = Ai /(h¯ γI H0 ) for the nucleus i leads to the well-established eq. (44) in the principal magnetic axes system

j 1 1 para pc j j δij = δijc + δij = Fi Sz j + (44) χzz − Tr χ j Gi + χxx − χyy Hi . 2NA 3 The contact and the pseudo-contact contributions are constituted by the product of two terms depending respectively on the lanthanide j (Sz j and χ j ) and on the nucleus i (Fi , Gi and Hi ). Since Sz j is poorly affected by crystal-ﬁeld effects, the values tabulated for the free ions (Golding and Halton, 1972; table 3) hold for all complexes and the contact term is easily factorized. On the other hand, χ j depends on the speciﬁc electronic structure of the lanthanide ion (4f n conﬁguration) combined with speciﬁc crystal-ﬁeld potentials produced by the surrounding ligands. Except for Bleaney’s approach (see sects. 2.3.1 and 2.4.2), no straightforward a priori prediction can be made for χ j and the treatment of pseudo-contact terms requires an initial assumption of the molecular structures in order to calculate a set of Gi and Hi which are then used to extract the anisotropic part of the paramagnetic susceptibility tensor (χzz − (1/3) Tr χ , χxx − χyy ) via least-squares ﬁtting processes (Forsberg, 1996). Non-linear least-square ﬁts may be further applied in order to simultaneously

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

373

reﬁne the geometrical factors and the components of the magnetic tensor (Forsberg, 1996; Peters et al., 1996). 2.4.1. Calculation of the anisotropic part of the magnetic susceptibility tensor with structural models In the absence of contact contribution (Fi = 0), the LIS purely reﬂects the pseudo-contact contributions and eqs. (27), (28) are ideally suited for extracting the experimental anisotropic part of the magnetic susceptibility tensor as long as a reasonable structural model is available. Kemple et al. (1988) reported a detailed 1 H NMR study of lanthanide complexes [R(indoleEDTA)] (R = La, Pr, Nd, Er, Yb) and [R(benzyl-EDTA)] (R = La, Pr, Yb, Lu; ﬁg. 3). Decoupling experiments, 2D-COSY spectra and relaxation measurements (T1 , T2 ) allowed an unambiguous assignment of the protons and reasonable molecular structures were obtained by molecular mechanics (MM2 force ﬁeld). Using an arbitrary Cartesian frame (x, y, z axes) with R(III) at the origin, the geometrical factors Gi and Hi were calculated from the polar coordinates (ri , θi and φi , ﬁg. 1). As a ﬁrst approximation, all contact contributions were set to zero and linear least-squares ﬁts according to eq. (27) for 13 aliphatic protons used as a basis gave the ﬁve components of the traceless part of the magnetic susceptibility tensor (χzz − (1/3) Tr χ , χxx − χyy , χxy , χyz , χyz ; 13 × 5 ﬁt). Diagonalisation of the latter tensor gave a set of Euler angles that relates the principal magnetic axes system to the original arbitrary Cartesian frame. The quality of the ﬁtting process for the complex of a lanthanide j is measured by the agreement factor AFj deﬁned in eq. (45) (Wilcott et al., 1972) i (δijobs − δijcalc )2 AFj = (45) . obs 2 i (δij ) Kemple et al. (1988) found AFPr = 0.147, AFNd = 0.346 and AFEu = 0.765 which were not satisfying and required corrections for the contact contributions of protons close to the metal centre. By introducing a minimal set of ﬁve different contact shifts for the protons of the acetate arms and of the ethylene bridge as ﬁtting parameters (δijc = Fi Sz j ), the original 13 observables × 5 ﬁtted parameters were transformed into a 13 × 10 ﬁt and multilinear least-squares ﬁts with eq. (44) gave AFPr = 0.032, AFNd = 0.031 and AFEu = 0.031. Since the contact contributions are obtained and adjusted as scalar parameters in eq. (44), any proton for which contact is allowed does not contribute to the determination of the magnetic

Fig. 3. Structures of substituted EDTA ligands.

374

C. PIGUET AND C.F.G.C. GERALDES

susceptibility tensor. Therefore, this approach requires a large number of protons sufﬁciently remote from the paramagnetic lanthanide and for which Fi = 0, but no assumption regarding the orientation of the molecular coordinates system and the principal magnetic axes system is required, a great advantage for low-symmetry complexes. Signiﬁcant rhombic distortions was observed for [R(indole-EDTA)] and [R(benzyl-EDTA)] (i.e., χxx − χyy = 0) and the orientation of the principal magnetic axes with respect to the molecular coordinates system varied for the different lanthanide complexes. Recently, Bertini et al. (2001) have applied this procedure for extracting the anisotropic part of the magnetic susceptibility tensor of the dicalcium protein calbindin D9k in which a lanthanide metal ion has been incorporated into the C-terminal calcium binding site. From 1097 pure pseudo-contact shifts (Fi = 0) combined with molecular modeling obtained by molecular mechanics, the anisotropic part of the magnetic susceptibility tensor χzz − (1/3) Tr χ and χxx − χyy (two parameters), together with the orientation of the principal magnetic axes (three parameters) have been determined for R = Ce–Yb, except Pm and Gd. Non-linear least-squares ﬁts simultaneously provide reﬁned positions for the NMR active nuclei. The average agreement factor AF = (1/n) nj=1 AFj for all lanthanides amounts to AF = 0.16. Forsberg et al. (1995) have developed a computer pc program which allows the systematic permutation of the observed pseudo-contact shifts (δij ) to different sets of protons when assignment is problematic. Basically following the procedure of Kemple et al. (1988), a structural model obtained by molecular mechanics is used for calculating the magnetic susceptibility tensor according to eq. (27) for each possible permutation. The associated agreement factors AFj (eq. (45)) are then used as criteria for selecting the most probable assignment which minimizes AFj . Subsequent diagonalisation or reorientation of the magnetic axes provides the anisotropic part of the magnetic susceptibility tensor in the principal magnetic axes system. Application to the axial C4 -symmetrical complexes [R(L11)]3+ (see sect. 3.2.3) by Forsberg et al. (1995) (R = Pr–Yb except Gd) has demonstrated that, as expected from symmetry arguments, the magnetic tensor is axially symmetric (χzz − (1/3) Tr χ = 3269 · 10−6 cgs · mol−1 and χxx − χyy = 0) and the z axis coincides with the molecular C4 axis (0.001◦ deviation). Ultimate reﬁnements of the molecular geometry requires the explicit consideration of contact contributions to the observed LIS and Forsberg et al. (1995) used a complicated approach in which χzz − (1/3) Tr χ , Gi and Fi are simultaneously varied in eq. (44) in order to minimize the agreement factor AF for n nuclei in m lanthanide complexes (n × m simultaneous equations). When one structural factor G1 is known from the structural model, a set of Fi values could be obtained which were used to extract pure pc para para pseudo-contact shifts according to δij = δij − δijc = δij − Fi Sz j . The ﬁnal reﬁnement of the structure then used least-squares ﬁts of eq. (29) in the principal magnetic axes system. In a parallel contribution, Lisowski et al. (1995a) used a closely related strategy for investigating the solution structures of the pseudo-axial texaphyrin complexes [R(texa)X2 ] (X = NO− 3, 1 diphenylphosphate; R = Ce–Yb except Pm and Gd) shown on ﬁg. 4. Pure H NMR pseudopc contact shifts δij were ﬁtted with eq. (28) by using the crystal structure of [Gd(texa)(NO3)2 ] as a structural model. Since the principal magnetic z and x axes were ﬁxed in the molecular symmetry Cs plane, only three parameters χzz − (1/3) Tr χ , χxx − χyy and an angle α deﬁning the location of the lanthanide metal above the average macrocyclic plane were varied by

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

375

Fig. 4. Structure and reference frame for the dimethoxy tetraethyl dimethyl trivalent lanthanide texaphyrin. The α angle measures the out-ofplane location of R(III) with respect to the mean macrocyclic plane (adapted from Lisowski et al. (1995a)).

using non-linear least-squares techniques in order to obtain the best ﬁt which minimized AFj for each complex (α is the angle between the x axis and the R–Ncentral pyrrole bond, ﬁg. 4). Systematic calculations with different sets of protons belonging to the complexes showed that the incorporation of the imino protons in the ﬁtting process signiﬁcantly increased AFj because contact contributions could not be neglected for these nuclei. Exclusion of the latter protons from the ﬁtting process gave 0.07 AFj 0.26, α angles in the range 5–30◦ and magnetic parameters χzz − (1/3) Tr χ and χxx − χyy of comparable magnitudes pointing to considerable rhombic distortion in each lanthanide complex. The latter result demonstrated that the intuitive assignment of pseudo-axial symmetry (i.e., C4 -symmetry) to the pc [R(texa)X2 ] is not justiﬁed. Computation of pure pseudo-contact shifts δij for the imino protons by using eq. (28) and the experimental magnetic anisotropy tensor in the principal magnetic axes system, allowed the separation of their contact contribution according to para pc eq. (44) (δijc = δij − δij = Fi Sz j ). Interestingly, plots of δijc vs free-ions Sz j values (table 3) showed the expected straight line (slope = Fi ) which conﬁrmed (i) the good quality of the calculated anisotropic part of the magnetic susceptibility tensor and (ii) the negligible dependence of Sz j on the crystal-ﬁeld splitting around room temperature. Lisowski et al. (1995b) proposed identical calculations for non-H atoms in [R(texa)X2 ] and were able to obtain reliable contact shifts for all 13 C and 31 P nuclei. Detailed σ and π -mechanisms for spin delocalisation could be addressed with this technique, but the main conclusions concerned the extreme sensitivity of both 31 P and 1 H chemical shifts to changes in axial ligations (X = nitrate or diphenylphosphate) which was mediated by the variation of the crystal-ﬁeld parameters affecting the magnetic susceptibility tensor. The direct experimental determination of the anisotropic part of the magnetic susceptibility tensor from a set of pure pseudo-contact shifts according to eqs. (27), (28) has the considerable advantage of requiring no assumption on the symmetry of the magnetic susceptibility tensor. Paramagnetic LIS for axial and rhombic complexes can be satisfyingly modeled. The estimation of the contact contributions either by simultaneous ﬁtting processes (Kemple et al.,

376

C. PIGUET AND C.F.G.C. GERALDES

1988) or by comparison with experimental LIS (Lisowski et al., 1995a, 1995b) allows a reliable separation of contact and pseudo-contact contributions. However, this approach requires (i) a large number of nuclei displaying pure pseudo-contact contributions and (ii) an accurate a priori structural model for the complex in solution, two conditions which are often limiting when considering supramolecular lanthanide complexes of intermediate size. 2.4.2. The model-free methods When no assumption is made on the solution structure, the determination of the desired geometrical factors Gi and Hi requires the a priori separation of the contact and pseudo-contact contributions to the LIS. Bleaney’s approach limited to the T −2 term and summarized by eqs. (40)–(42) (see sect. 2.3.1) is well-suited for this purpose since the anisotropic part of the magnetic susceptibility tensor can be modeled by a judicious combination of an electronic factor depending only on the electronic conﬁguration of the lanthanide j (i.e., Bleaney’s factors Cj in table 3) and the crystal-ﬁeld parameters of rank two for the complexes. Substituting the pseudo-contact contribution of eq. (42) into eq. (44) gives eq. (46) which reduces to eq. (47) for axial systems (B22 = 0, Reilley et al. (1975), Bryden and Reilley (1982)). Interestingly, the spherical crystal-ﬁeld operator C22 and the associated B22 parameter are not involved for systems possessing at least a C3 axis (Görller-Walrand and Binnemans, 1996) and eq. (47) also holds for lanthanide complexes displaying trigonal symmetry. We have consequently limited the complexes considered in this review to those possessing at least a C3 or a C4 axis and for which effective axial symmetry can be applied (eq. (47)). It is worth noting that the assignment of axial symmetry to trigonal complexes is valid when the T −n series is limited to n = 2 (Bleaney’s hypothesis, Bleaney (1972)), but it can be extended for n = 3 because the third-order coefﬁcient of the rhombic term (Hi ) still vanishes when all Bqk are zero except B20 , B04 , B06 , B34 , B36 and B66 (McGarvey, 1979) √

para pc δij = δijc + δij = Fi Sz j + Cj B02 Gi + 6B22 Hi , (46) para

δij

= Fi Sz j + Cj B02 Gi .

(47)

2.4.2.1. Reilley’s method. Since Sz j and Cj do not depend on the crystal-ﬁeld splitting (see sects. 2.2 and 2.3.1), Reilley et al. (1975) ﬁrst proposed to rearrange eq. (46) into two linear forms (eqs. (48), (49)) for testing isostructurality along the lanthanide series para

δij

Sz j para

δij

Cj

= Fi +

√ Cj 2 B0 Gi + 6B22 Hi , Sz j

√

Sz j = B02 Gi + 6B22 Hi + Fi . Cj

(48) (49)

Although these two equations are mathematically identical, eq. (48) should be used when para para δij is dominated by the pseudo-contact contribution and eq. (49) should be used when δij is dominated by contact effects, thus maximizing the slopes of the resulting straight lines para para (Reuben and Elgavish, 1980). Plots of δij /Sz j vs Cj /Sz j (eq. (48)) or δij /Cj vs

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

377

Sz j /Cj (eq. (49)) along the lanthanide series at a ﬁxed temperature are expected to give straight lines √ and any deviations point to structural changes affecting the ‘structural term’ B02 Gi + 6B22 Hi (Reilley et al., 1975; Sherry and Geraldes, 1989). However this simple interpretation assumes that (i) the hyperﬁne constant (Ai and hence the Fi term) and the crystal-ﬁeld parameters B02 and B22 do not vary along the lanthanide series, (ii) the T −2 term is sufﬁcient for describing the molecular magnetic anisotropy and (iii) the stepwise lanthanide contraction occurring when going from R = Ce to Yb has negligible effects on the structural term. Peters (1986) has theoretically addressed the last point and geometrical Gi factors for axial complexes modeled with molecular mechanics have been computed. The smooth contraction of the R–ligand distances often results in a minor break occurring between R = Eu para and R = Tb in the plot of δij /Sz j vs Cj /Sz j because the monotonous change in Gi is ampliﬁed by the large values of Cj characterising the second part of the lanthanide series para (table 3). It is thus concluded that both linear plots δij /Sz j vs Cj /Sz j (eq. (48)) and para δij /Cj vs Sz j /Cj (eq. (49)) should simultaneously display a break along the lanthanide series to be indicative of a signiﬁcant structural change (ﬁg. 5). 2.4.2.2. Crystal-ﬁeld independent methods. The invariance of crystal-ﬁeld parameters is more problematic since the experimental Bqk parameters of lanthanide complexes in the solid state usually exhibit signiﬁcant variations along the lanthanide series resulting from the contraction of the 4f orbitals (Freeman and Watson, 1962; Görller-Walrand and Binnemans, 1996). Moreover, an abrupt change around the middle of the series, sometimes referred to as the ‘gadolinium break’ effect has been evidenced in Na3 [Yb1−x Rx (L7 –2H)3]·NaClO4 ·10H2 O (see sect. 3.1.7, Hopkins et al. (1996)), and Na3 [R(L1 –2H)3 ]·2NaClO4 ·6H2 O (see sect. 3.1.1, Hopkins et al. (1998)). Related effects are thus expected for lanthanide complexes in solution and efforts have been made to remove the inﬂuence of crystal-ﬁeld parameters (Reuben, 1982; Spiliadis and Pinkerton, 1982). In axial complexes (i.e., possessing at least a C3 axis),1 the simultaneous consideration of the chemical shifts of two nuclei i and k provides two equations (eqs. (47), (50)) from which Bleaney’s factor Cj and the crystal ﬁeld parameter B02 can be removed by a judicious mathematical substitution in order to give eq. (51) (Spiliadis and Pinkerton, 1982; Platas et al., 1999) para

δkj = Fk Sz j + Cj B02 Gk , para para δij Gi Gi δkj + = Fi − Fk · . Sz j Gk Gk Sz j para

para

(50) (51)

Plots of δij /Sz j vs δkj /Sz j are ideally suited for testing structural changes occurring along the lanthanide series in axial complexes because straight lines are expected as long as the slope Rik = Gi /Gk and the intercept Fi − Fk Rik do not vary. Structural changes affect the slope Rik =

Gi (3 cos2 θi − 1) rk3 · = Gk (3 cos2 θk − 1) ri3

1 All complexes for which effective axial symmetry can be applied (eq. (47), see sect. 2.4.2).

378

C. PIGUET AND C.F.G.C. GERALDES

para

Fig. 5. Plots of (a) δij /Sz j vs Cj /Sz j para

(eq. (48)) and (b) δij /Cj vs Sz j /Cj (eq. (49)) for the carboxylate carbons in simulated nine-coordinate tricapped trigonal prismatic [R(OOCCH)3 (OH2 )3 ] complexes (redrawn from Peters (1986)).

and can be easily detected, but crystal-ﬁeld changes which are not associated with signiﬁcant structural variations have no effect. Changes in the intercept are more difﬁcult to interpret since Fi − Fk Rik depends on geometrical factors (via Rik ) and hyperﬁne constants (via Fi and Fk ). In favourable cases, the prior analysis of the slope Rik allows to draw reliable conclusions concerning possible variations of the hyperﬁne constants along the lanthanide series (Platas et al., 1999; Rigault et al., 2000b). Although Sz j is relatively independent from crystalﬁeld effects around room temperature (see sect. 2.2), Geraldes et al. (2001) have proposed to remove it by solving simultaneously eqs. (47), (50), (52) for three different nuclei i, k, l in the same lanthanide complex. Straightforward algebraic substitutions and transformations give eq. (53) where Rik = Gi /Gk and Sik = Fi /Fk para

δlj

= Fl Sz j + Cj B02 Gl ,

(52)

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS para

δij

para

δkj

para

= para

(Slk Rik − Sik Rlk ) (Sik − Rik ) δlj + · para . (Slk − Rlk ) (Slk − Rlk ) δkj para

Plotting δij /δkj of slope α=

379

para

para

against δlj /δkj

(53)

along the lanthanide series should yield a straight line

(Sik − Rik ) (Slk − Rlk )

and an intercept β=

(Slk Rik − Sik Rlk ) , (Slk − Rlk )

provided that Sik , Slk , Rik and Rlk are invariant. Since the simple eq. (53) only requires experimental LIS data for testing isostructurality, its use seems promising as long as three different NMR-active nuclei are available in the complex. However, both the slope (α) and the intercept (β) are complicated non-linear combinations of geometrical Gi factor and contact Fi terms. Deviations from linearity are difﬁcult to interpret and accidental compensation effects cannot be ruled out when strict linear behaviours are observed (Ouali et al., 2002). 2.4.2.3. The special case of rhombic systems. The removal of crystal-ﬁeld parameters according to the two-nuclei (eq. (51)) and the three-nuclei (eq. (53)) methods is strictly limited to axial complexes for which eq. (47)√holds (i.e., possessing at least a C3 axis). The explicit consideration of the rhombic term Cj 6B22 Hi in Bleaney’s approach (eq. (42)) signiﬁcantly complicates the derivation of crystal-ﬁeld independent equations which requires at least three different nuclei. To the best of our knowledge, no analytical form has been reported in the literature for rhombic systems. Reuben and Elgavish (1980) have suggested that eq. (42) is only a poor approximation for rhombic systems and a better modeling of the pseudo-contact contribution requires two experimental factors Cjaxial and Cjrhombic (eq. (54)), pc

δi = Cjaxial Gi + CjrhombicHi .

(54)

Since Cjaxial is proportional to χzz − (1/3) Tr χ and Cjrhombic is proportional to χxx − χyy in the principal magnetic axes system (eq. (28)), Reuben and Elgavish (1980) used the experimental diagonalised magnetic susceptibility tensors reported by Horrocks and Sipe (1972) for solidstate [R(dipivaloymethane)3(4-picoline)2] complexes in order to compute the proportionality axial = −100. Interestingly they notice that the axial factors Cjaxial and Cjrhombic scaled to CDy factors Cjaxial satisfyingly match original Bleaney’s Cj factors, but Cjrhombic have only poor correlations with Cj pointing to the limit of theoretical Bleaney’s approach which predicts a single factor (Cjaxial = Cjrhombic , eq. (42), table 3). Two linear forms (eqs. (55), (56)) can be derived from eq. (54) for nuclei displaying no contact contributions (Fi = 0) pc

δi

Cjaxial

= Gi + H i

Cjrhombic Cjaxial

,

(55)

380

C. PIGUET AND C.F.G.C. GERALDES pc

δi

Cjrhombic pc

= H i + Gi

Cjaxial Cjrhombic

(56)

. pc

Plots of δi /Cjaxial vs Cjrhombic/Cjaxial (eq. (55)) or δi /Cjrhombic vs Cjaxial /Cjrhombic (eq. (56)) are expected to be linear within an isostructural series. The ﬁtting process has been applied to non-axial lanthanide shifts reagents and leads to improved linear correlations (Reuben and Elgavish, 1980), but the origin of the deviation from the strict T −2 terms was not addressed. We can infer that the different behaviours of Cjaxial and Cjrhombic along the lanthanide series result from higher-order T −n terms (n 3) which are neglected in original Bleaney’s approach, but which are required to reliably model complexes possessing large crystal-ﬁeld splittings (ECF /kT < 1). Since the Cjrhombic factors proposed by Reuben and Elgavish (1980) originate from the speciﬁc crystal-ﬁeld splitting of one reference complex [R(dipivolymethane)3(4-picoline)2], their systematic use for all lanthanide complexes is doubtful and this approach, to the best of our knowledge, has not been put on again for the structure-independent analysis of LIS data.

3. Application of the model-free methods to axial monometallic lanthanide complexes with sterically rigid ligands The three following criteria have been selected for discussing the application of the model-free methods to lanthanide complexes. (1) Lanthanide complexes with axial symmetry (i.e., possessing at least a threefold axis, see sect. 2.4.2) are exclusively considered because the principal magnetic z axis coincides 2 spherical tensor with the molecular symmetry axis (Forsberg et al., 1995) and the C±2 operators do not contribute to the crystal-ﬁeld potentials√(Görller-Walrand and Binnemans, 1996). The rhombic term of Bleaney’s approach 6B22 Hi (eqs. (42), (46)) thus vanishes and the crystal-ﬁeld independent methods (eqs. (51), (53)) can be used without complications. (2) The use of sterically rigid ligands ensures the formation of well-deﬁned coordination spheres which strongly limit dynamic behaviours occurring in solution on the NMR time scale. (3) Multidentate chelating ligands produce stable lanthanide complexes in solution. At concentrations compatible with NMR measurements, partial decomplexation is negligible and exchange processes involving either the free ligand or complexes with different stoichiometries are ignored because highly unequally populated sites do not signiﬁcantly affect NMR spectra (Pons and Millet, 2001). Under these conditions, the experimenpara tal paramagnetic lanthanide-induced chemical shifts δij are obtained directly from the NMR spectra recorded under the slow-exchange regime at a single concentration. When signiﬁcant decomplexation occurs (see sect. 3.1.1), the shifts for bound ligands can be extrapolated from fast-exchange NMR spectra recorded upon successive additions of small portions of R(III) to the ligand solution (Peters et al., 1996).

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

381

3.1. Complexes with threefold symmetry 3.1.1. [R(L1 –2H)3 ]3− (L1 = oxydiacetic acid) The thermodynamic properties of the successive complexes [R(L1 –2H)n ](3−2n)+ (n = 1, 2, 3) in water have been studied extensively by Grenthe (1973) and the associated cumulative stability constants βn show only limited stability for the D3 -symmetrical triple-helical complexes [R(L1 –2H)3 ]3− in solution (Martell and Smith, 1977). For a total ligand concentration of 0.2 mol · dm−3 and a stoichiometric ratio La/[L1–2H]2− = 0.33, one calculates the following ligand distribution: [La(L1–2H)3 ]3− (91%), [La(L1 –2H)2 ]− (6%) and [L1 –2H]2− (3%). As decomplexation cannot be completely neglected, Peters (1988) has extrapolated experimenpara tal paramagnetic shifts for bound ligands δij for [R(L1 –2H)3 ]3− (R = La–Lu, except Pm and Gd) from fast-exchange spectra at 346 K (0.067 mol · dm−3 in water). The observed 1 H, 13 C and 17 O NMR data conﬁrm the formation of D -symmetrical triple-helical complexes 3 [R(L1 –2H)3 ]3− in solution in agreement with the solid-state crystal structures reported for Na3 [R(L1 –2H)3]·2NaClO4 ·6H2 O (R = La–Lu) which show R(III) to be coordinated by nine oxygen donors in pseudo-tricapped trigonal prismatic arrangements (Hopkins et al., 1998; ﬁg. 6). Interestingly, Peters (1988) notices that the methylene protons are enantiotopic for the light lanthanides (R = Ce–Dy) and become diastereotopic for R = Ho–Yb which implies a dynamic intramolecular interconversion between the two helical enantiomers P -[R(L1 – 2H)3 ]3− M-[R(L1 –2H)3 ]3− occurring at a moderate rate on the NMR time scale. The observation of two resolved signals for the methylene protons for the heavy lanthanides R = Ho–Yb reﬂects the larger pseudo-contact contributions induced in the second part of the lanthanide series and a slower exchange rate due to stronger lanthanide–ligand bonds. A rough estimate of G= = 54 kJ/mol is obtained from the measurements of the coalescence temperatures for R = Tm, Yb. In excess of ligand (R/[L1 –2H]2− < 0.33), fast dynamic intermolecular processes involving ligand exchanges in the ﬁrst coordination sphere are also detected on the NMR time scale. At a given temperature, the rate of ligand exchange de-

Fig. 6. Schematic formation of the D3 -symmetrical complexes [R(L1 –2H)3 ]3− in water. The representation of [R(L1 –2H)3 ]3− corresponds to the crystal structure of Na3 [Eu(L1 –2H)3 ]·2NaBF4 ·6H2 O (adapted from Fronczek et al. (1981)).

382

C. PIGUET AND C.F.G.C. GERALDES

para

para

Fig. 7. Plots of δij /Sz j vs Cj /Sz j (eq. (48)) and δij /Cj vs Sz j /Cj (eq. (49)) along the lanthanide series for various nuclei in [R(L1 –2H)3 ]3− (water, 346 K). (a) Carbon of the carbonyl group, (b) carbon of the methylene group, (c) protons of the methylene groups (redrawn from Peters (1988)).

para

para

creases with decreasing size of R(III). Plots of δij /Sz j vs Cj /Sz j (eq. (48)) and δij /Cj vs Sz j /Cj (eq. (49)) along the lanthanide series for [R(L1 –2H)3 ]3− show scattered diapara grams for which unambiguous linear correlations are limited to δij /Sz j vs Cj /Sz j with R = Ce–Eu (ﬁg. 7). Surprisingly, Bleaney’s factors Cj determined at 300 K (table 3) are used without corrections for the treatment of the experimental NMR data recorded at 343 K. This approximation is probably justiﬁed for most R(III) except for R = Sm and Eu (see sect. 2.3), but the poor para correlations exhibited by the δij /Cj vs Sz j /Cj plots might result from inadequate values of Cj (the Sm(III) data have been excluded from the mathematical analysis, but the Eu(III) data have been considered, ﬁg. 7). The abrupt break of the plots according to eq. (48) occurring near the middle of the series (i.e., between R = Eu and R = Tb) is ascribed to a structural change involving nine-coordinate D3 -symmetrical complexes [R(L1 –2H)3 ]3− similar to those found in the crystal structure for R = Ce–Eu, and eight-coordinate complexes [R(L1 –2H)3 ]3− with low symmetry for R = Tb–Yb. Since the three ligands remain equivalent on the NMR time scale for R = Tb–Yb, Peters (1988) proposes fast on-off equilibria of the non-coordinated carboxylate group (ﬁg. 8).

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

383

Fig. 8. Schematic representation of the two different solutions structures observed by NMR for [R(L1 –2H)3 ]3− (adapted from Peters (1988)).

These results strongly contrast with solid-state structures of Na3 [R(L1 –2H)3]·2NaClO4 · 6H2 O (R = La–Lu) in which similar nine-coordinate R(III) ions are located at sites of D3 point-group symmetry along the complete lanthanide series (Hopkins et al., 1998). On the other hand, detailed spectroscopic investigations performed on these crystals provide crystalﬁeld parameters Bqk (k = 2, q = 0; k = 4, q = 0, 3; k = 6, q = 0, 3, 6; R = Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er) which exhibit the expected monotonous decrease of the crystal-ﬁeld interaction strength SCF along the lanthanide series (contraction of the 4f electron charge distribution, Carnall et al., 1989). However, an unexpected abrupt variation of SCF (mainly due to Bqk of rank four and six) is detected near the middle of the lanthanide series (Hopkins et al., 1998; ﬁg. 9).

Fig. 9. Plot of the crystal-ﬁeld interaction strength quantities SCF =

1 1 k 2 k 2 for k 2k+1 (B0 ) + 2 m>0 |Bm | 3

eight Na3 [R(L1 –2H)3 ]·2NaClO4 ·6H2 O systems (redrawn from Hopkins et al. (1998)).

384

C. PIGUET AND C.F.G.C. GERALDES

Fig. 10. Crystal-ﬁeld independent plot of para para δij /Sz j vs δkj /Sz j (eq. (51)) for the carbon (CH2 ) and the protons (CH2 ) of the methylene groups in [R(L1 –2H)3 ]3− (D2 O, 346 K, drawn from data reported by Peters (1988)).

Although the Bqk parameters obtained in the solid state are only indicative for those relevant in solution, their abrupt variations near the middle of the series is expected to produce a break para in the linear plot δij /Sz j vs Cj /Sz j according to eq. (48) without resorting to a major structural change. To the best of our knowledge, no analysis of these data using the crystalpara ﬁeld independent two-nuclei technique (eq. (51)) has been reported, but plots of δij /Sz j para vs δkj /Sz j based on the data reported by Peters (1988) suggest the existence of a single straight line for R = Ce–Yb compatible with an approximate isostructural series in solution (ﬁg. 10). Since geometrical factors Gi calculated from the crystal structure of Na3 [Ce(L1 – 2H)3 ]·2NaClO4 ·6H2 O closely match those found in solution for R = Ce–Eu (Peters, 1988), we can tentatively infer that no major structural change indeed occurs in solution and the ninecoordinate D3 -symmetrical structure found in the solid-state is a satisfying model for [R(L1 – 2H)3 ]3− along the complete lanthanide series in water. The abrupt break near the middle of the series originates from variations of the crystal-ﬁeld parameters which parallel those evidenced in the solid-state. 3.1.2. [R(L2 )3 ]3+ (L2 = 2,6-bis(benzimidazole)pyridine) The tridentate ligand L2 possesses heterocylic nitrogen donors exhibiting only a limited afﬁnity for R(III), and no complexation occurs in water. However, efﬁcient coordination is restored in less competing solvents leading to the successive formation of [R(L2 )n ]3+ (n = 1, 2, 3) in acetonitrile (Piguet et al., 1993). The two ﬁrst successive stability constants Kn (n = 1, 2) show only minor variations along the lanthanide series, while K3 increases with increasing atomic number, reaches a maximum around R = Gd(III) and suddenly decreases, eventually producing poorly stable [R(L2 )3 ]3+ complexes for the smaller lanthanides (Petoud et al., 1997). This fascinating size-discriminating effect favouring the complexation of mid-range R(III), results from the modulation of intramolecular interstrand interactions involving π –π stacking between aromatic benzimidazole groups in the D3 -symmetrical [R(L2 )3 ]3+ complexes (ﬁg. 11). For the large lanthanides (R = La–Gd), attractive interstrand π -stacking stabilizes the ﬁnal triple helical complexes, but further contraction of the ionic radii for R = Tb– Lu induces considerable repulsive van der Waals interactions.

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

385

Fig. 11. Schematic formation of the D3 -symmetrical complexes [R(L2 )3 ]3+ in acetonitrile with numbering scheme. The representation of [R(L2 )3 ]3+ corresponds to the crystal structure of [Eu(L2 )3 ](ClO4 )3 (Piguet et al., 1993).

For large concentrations of ligand compatible with NMR measurements ( 0.015 mol · dm−3 ), the stability constants predict that [R(L2 )3 ]3+ are quantitatively formed (> 98%) for R = Ce–Tb. For smaller lanthanides, partial decomplexation occurs as demonstrated by the appearance of small new peaks in the spectrum of [Dy(L2)3 ]3+ (Petoud et al., 1997). Although NMR spectra show three sets of resolved signals corresponding to [Dy(L2)3 ]3+ , [Dy(L2)2 ]3+ and L2 under slow-exchange regime at 298 K, the authors have restricted their analysis to R = Ce–Dy. As inferred from the crystal structure of [Eu(L2)2 ]3+ , the 1 H and 13 C NMR data demonstrate that the threefold symmetry is maintained in solution. Moreover, the replacement of methyl groups in L2 by ethyl groups in L2a provides diastereotopic probes in [R(L2a )3 ]3+ which systematically display two separated signals for the methylene protons in complete agreement with the expected helical wrapping of the strands and an average D3 point group para para symmetry in solution. Plots of δij /Sz j vs Cj /Sz j (eq. (48)) and δij /Cj vs Sz j /Cj (eq. (49)) for [R(L2 )3 ]3+ (R = Ce–Dy) give linear correlations arising from a single isostructural series (ﬁg. 12). Multi-linear least-square ﬁts of eq. (47) using Sz j and Cj factors of table 3 provide contact Fi and pseudo-contact B02 Gi terms collected in table 4. The agreement factor AFi for a nucleus i for an isostructural series of n different lanthanide complexes is given by eq. (57) (Wilcott et al., 1972) n j =1 (δijobs − δijcalc )2 AFi = (57) . n obs 2 j =1 (δij ) The AFi factors for [R(L2 )3 ]3+ (R = Ce–Dy) are satisfying except for C2 and C3 which undergo minor to negligible paramagnetic shifts (table 4). Interestingly, the sizeable Fi terms (i.e., hyperﬁne constants) observed for H1 and H5 suggest signiﬁcant spin delocalisation for nuclei separated by four bonds from the paramagnetic centre, an effect ascribed to efﬁcient delocalisation within heterocylic N-donor ligands (Petoud et al., 1997). For H3 and C3, the pseudo-contact terms B02 Gi are only marginally different from zero in complete agreement with their location close to the magic angle θi = 54.7◦ for which Gi = 0 (θC3 = 57.8◦ and

386

C. PIGUET AND C.F.G.C. GERALDES

para

para

Fig. 12. Plots of (a) δij /Sz j vs Cj /Sz j (eq. (48)) and (b) δij /Cj vs Sz j /Cj (eq. (49)) for H5 in [R(L2 )3 ]3+ (R = Ce–Dy, CD3 CN, 298 K, drawn from data reported by Petoud et al. (1997)). Table 4 Computed values for contact (Fi ), pseudo-contact (B02 Gi ) terms and agreement factors (AFi ) for 1 H- and 13 C-nuclei in complexes [R(L2 )3 ]3+ (R = Ce–Dy, CD3 CN, 298 K, Petoud et al. (1997)). See ﬁg. 11 for the atom-numbering scheme Fi B02 Gi AFi Fi B02 Gi AFi

H1 −0.41(12) 0.87(4) 0.04 C1 0.26(10) 0.25(3) 0.08

H2 −0.05(2) 0.094(7) 0.06 C2 −0.26(4) 0.11(1) 0.25

H3 −0.006(5) −0.008(2) 0.05 C3 0.07(3) 0.002(9) 0.25

H4 0.16(1) −0.111(3) 0.06 C4 0.33(2) −0.124(7) 0.12

H5 0.42(6) −0.30(2) 0.10 C5 3.38(19) −0.46(6) 0.07

H6 0.26(4) −0.22(1) 0.08 C6 −0.93(14) −0.30(5) 0.06

CH3 0.14(3) −0.25(1) 0.05 CH3 0.36(3) −0.28(1) 0.06

θH3 = 59◦ in the crystal structure of [Eu(L2)3 ]3+ ). Although no analysis of these data using the crystal-ﬁeld independent two-nuclei technique (eq. (51)) has been reported, plots of para para δij /Sz j vs δkj /Sz j based on the data reported by Petoud et al. (1997) suggest the existence of a single straight line for R = Ce–Dy, thus conﬁrming isostructurality (ﬁg. 13). j Finally, the anisotropic part of the axial magnetic susceptibility tensor χzz − (1/3) Tr χ j has been computed following the method of Kemple et al. (1988) applied to axial complexes for which the principal magnetic z axis corresponds to the molecular threefold axis. Equation (44) reduces to eq. (58) and multi-linear least-squares ﬁts based on geometrical factors Gi obtained from the crystal structure of [Eu(L2)3 ]3+ and using 13 paramagnetic shifts and eleven contact j contributions (all carbons and ﬁve protons, 13 × 11 ﬁts) give magnetic anisotropies χzz − j (1/3) Tr χ which display only qualitative agreement with Bleaney’s factor Cj (Petoud et al., 1997). This poor correlation is not diagnostic for the rejection of Bleaney’s approach, but it can be assigned to the very limited set of nuclei (H2 and H3) for which pure pseudocontact contributions are observed and which are prominent for the calculation of the magnetic

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

387

Fig. 13. Crystal-ﬁeld independent para para plot of δij /Sz j vs δkj /Sz j (eq. (51)) for the C5–H5 pair in [R(L2 )3 ]3+ (R = Ce–Dy, CD3 CN, 298 K, drawn from data reported by Petoud et al. (1997)).

anisotropy para δij

= δijc

pc + δij

= δijc

1 + 2NA

1 j j χzz − Tr χ Gi . 3

(58)

The authors conclude that [R(L2 )3 ]3+ (R = Ce–Dy) are isostructural in solution and adopt a structure reminiscent to that found in the crystal structure of [Eu(L2)3 ]3+ . The aromatic backbone acts as an efﬁcient relay for spin delocalisation and/or spin polarization which allows contact contributions to operate at long distances. 3.1.3. [R(L3 )3 ]3+ (L3 = 2,6-pyridinedicarboxylic acid-bis-diethylamide) The replacement of the two benzimidazole side arms of L2 by two neutral carboxamide groups in L3 provides a tridentate NO2 chelate which exhibits signiﬁcant afﬁnity for R(III) in acetonitrile despite its increased ﬂexibility (Renaud et al., 1997). The stability constants for the complexes [R(L3 )n ]3+ (R = La–Lu, n = 1, 2, 3) are comparable to those found for light lanthanides with L2 ([R(L2 )n ]3+ , R = La–Gd, n = 1, 2, 3), but K3 for [R(L3 )3 ]3+ monotonously increases when going from Gd to Lu in agreement with the well-known electrostatic trend (Choppin, 1989). No speciﬁc size-discriminating effect is detected and the triple helical complexes [R(L2)3 ]3+ are quantitatively formed ( 98%) in acetonitrile for a total ligand concentration of 0.15 mol · dm−3 and R/L3 = 0.33 (Renaud et al., 1997). The 1 H and 13 C NMR data imply the existence of three equivalent ligand strands on the NMR time scale and the separated 1 H NMR signal detected for the methylene protons of the ethyl groups of the carboxamide side arms (R = Y, Lu) points to the formation of D3 -symmetrical complexes in solution reminiscent of the crystal structures obtained for [R(L3 )3 ]3+ (R = La, Eu, ﬁg. 14). Variable-temperature NMR measurements for [R(L3 )3 ]3+ (R = La, Sm, Y, Lu) in acetonitrile ﬁrmly establish dynamic interconversion between the D3 -symmetrical helical enantiomers P -[R(L3 )3 ]3+ M-[R(L3 )3 ]3+ . The coalescence temperature increases with de-

388

C. PIGUET AND C.F.G.C. GERALDES

Fig. 14. Schematic formation of the D3 -symmetrical complexes [R(L3 )3 ]3+ in acetonitrile with numbering scheme. The representation of [R(L3 )3 ]3+ corresponds to the crystal structure of [Eu(L3 )3 ](CF3 SO3 )3 (THF)2 (Renaud et al., 1997).

creasing ionic radii and the calculated free energies of activation at these temperatures follow the same trend G= (Sm, T = 263 K) = 55 kJ/mol, G= (Y, T = 318 K) = 73 kJ/mol and G= (Lu, T = 333 K) = 78 kJ/mol. For R = La, the coalescence temperature lies below 233 K and only a maximum activation energy can be estimated (G= (La) < 55 kJ/mol). para para Plots of δij /Sz j vs Cj /Sz j (eq. (48)) and δij /Cj vs Sz j /Cj (eq. (49)) for 1 H and 13 C NMR data of [R(L3 ) ]3+ (R = Ce–Yb, except Pm, Gd, Dy, Ho) display an abrupt de3 viation from linearity between R = Tb and R = Er and require two different straight lines (ﬁg. 15). Two different isostructural series are considered for R = Ce–Tb and Er–Yb, and two sets of contact Fi and pseudo-contact B02 Gi terms are obtained according to least-squares ﬁts of eq. (47) (table 5, Renaud et al. (1997)).

para

para

Fig. 15. Plots of (a) δij /Sz j vs Cj /Sz j (eq. (48)) and (b) δij /Cj vs Sz j /Cj (eq. (49)) for H2 in [R(L3 )3 ]3+ (R = Ce–Yb, CD3 CN, 298 K, redrawn from Renaud et al. (1997)).

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

389

Table 5 Computed values for contact (Fi ), pseudo-contact (B02 Gi ) terms and agreement factors (AFi ) for 1 H- and 13 C-nuclei in complexes [R(L3 )3 ]3+ (R = Ce–Yb, CD3 CN, 298 K, Renaud et al. (1997)). See ﬁg. 14 for the atom-numbering scheme

Fi B02 Gi AFi Fi B02 Gi AFi

Fi B02 Gi AFi Fi B02 Gi AFi

H2 0.129(4) −0.177(2) 0.01 C3 −1.02(3) −0.22(1) 0.02

H3 0.11(1) −0.160(5) 0.04 C4 0.6(1) 0.16(5) 0.11

H2 0.110(1) −0.054(1) 0.00 C3 −0.82(2) −0.072(1) 0.01

H3 0.14(1) −0.044(4) 0.02 C4 1.1(4) −0.4(1) 0.08

Series R = Ce–Tb H6 H8 0.023(7) 0.00(2) −0.006(3) 0.118(6) 0.49 0.05 C5 C6 0.31(5) −0.07(3) 0.00(2) 0.064(9) 0.13 0.20 Series R = Er–Yb H6 H8 0.01(1) −0.26(9) −0.003(4) −0.01(3) 0.33 0.20 C5 C6 −0.21(2) −0.267(4) −0.045(4) −0.014(1) 0.06 0.01

C1 0.25(9) −0.53(4) 0.07 C7 0.23(5) 0.02(2) 0.16

C2 3.01(9) −0.40(3) 0.04 C8 −0.11(3) 0.06(1) 0.31

C1 0.9(4) −0.14(9) 0.13 C7 0.19(6) 0.03(2) 0.24

C2 2.495(1) −0.034(1) 0.00 C8 0.30(4) 0.09(1) 0.13

The signiﬁcant hyperﬁne constants (Fi terms) observed for the protons of the pyridine ring (H2 and H3) parallel those reported for [R(L2 )3 ]3+ and conﬁrms efﬁcient spin delocalisation onto the heterocyclic aromatic ring. Attempts to extract the axial magnetic anisotropies j χzz − (1/3) Tr χ j with eq. (58) and using the crystal structure of [Eu(L3)3 ]3+ as a model only fail because pure pseudo-contact contributions are limited to the two terminal methyl protons. Their versatile locations within each strand in the crystal structure of [Eu(L3)3 ]3+ do not allow the calculation of reliable D3 -average geometrical Gi factors. The crystal-ﬁeld and structure-independent method (eq. (51)) has been applied for unambiguously demonstrating para para that a structural change occurs along the lanthanide series. Plots of δij /Sz j vs δkj /Sz j indeed display systematic abrupt breaks between R = Tb and Er leading to two different sets of structural terms Rik = Gi /Gk (ﬁg. 16, Rigault et al. (2000a)). Comparison between Rik terms observed in solution and those calculated from the crystal structure of [Eu(L3)3 ]3+ shows only limited agreement (table 6), but quantitative statistical analyses suggest that the regular triple-helical arrangement of the strands observed in the solid state better ﬁts the solution structure of the light lanthanides (R = Ce–Tb, Rigault et al. (2000a)). It was noticed that the dramatic discrepancies observed for pairs involving the C4 atom result from its location close to the magic angle (θC4 = 54.9◦ in the crystal structure of [Eu(L3)3 ]3+ ). Since GC4 ≈ 0, extreme sensitivity of RC4,k terms for minor structural changes is expected. Finally, Renaud et al. (1997) have used relaxation measurements and eq. (18) to extract R–Hi and R–Ci distances which indeed slightly differ for R = Ce and R = Yb. Renaud et al. (1997) and Rigault et al. (2000a) conclude that a structural change is ﬁrmly established for [R(L3 )3 ]3+ near the

390

C. PIGUET AND C.F.G.C. GERALDES

Fig. 16. Crystal-ﬁeld independent plot of para para δij /Sz j vs δkj /Sz j (eq. (51)) for the C2–H2 pair in [R(L3 )3 ]3+ (R = Ce–Yb, acetonitrile, 298 K, redrawn from Rigault et al. (2000a)). Table 6 para para Minimal set of structural term Rik = Gi /Gk obtained from plots of δij /Sz j vs δkj /Sz j according to eq. (51) 3 3+ a for [R(L )3 ] (CD3 CN, 298 K) (Rigault et al., 2000a). See ﬁg. 14 for the atom-numbering scheme Rik (Ce–Tb)b Rik (Er–Yb)c Rik ([Eu(L3 )3 ]3+ )d

H2–H3 0.93(5) 1.02(9) 1.018

H2–C1 0.33(3) 0.14(8) 0.213

H2–C2 0.39(3) 1.38(6) 0.499

H2–C3 0.91(4) 0.65(4) 0.591

H2–C4 −0.7(3) 0.08(2) 16.321

a A complete set of R data can be generated according to R = R · R . ik ik im mk b Values for the ﬁrst isostructural series (Sm has been removed because of its faint paramagnetism). c Values for the second isostructural series. d Calculated from the crystal structure of [Eu(L3 ) ](CF SO ) (THF) . 3 3 3 3 2

middle of the lanthanide series. Its assignment to speciﬁc variations of structural parameters in the triple-helical complexes has been delayed until a similar behaviour observed by Ouali et al. (2002) for [R(L7 –2H)3 ]3− , could be ascribed to fast oscillations of the central pyridine ring occurring for large R(III) ions, R = Ce–Tb, a process which also affects [R(L3 )3 ]3+ (see sect. 3.1.7 and ﬁg. 33). 3.1.4. [R(L4 )]3+ and [R(L4 +H)]4+ (L4 = tris{2-[N -methylcarbamoyl(6-(N ,N -diethylcarbamoyl)pyridine-2)ethyl]amine}) In order to limit ﬂexibility, three tridentate binding units similar to L3 have been connected to a covalent tri(2-aminoethyl)amine (TREN) tripod to give the nonadentate podand L4 . Upon reaction with R(III) (R = La–Eu, Yb, Lu, Y) in acetonitrile/nitromethane (1:1), the NMR spectra conﬁrm the formation of the expected C3 -symmetrical complexes [R(L4 )]3+ (Renaud et al., 1999). The methylene protons are systematically diastereotopic at 298 K. For the diamagnetic cations R = Y, Lu, no coalescence is observed in the accessible temperature range (233–343 K), but the rate of helical interconversion increases with increasing ionic radii and [La(L4)]3+ shows coalescence at 323 K, thus pointing to a fast P -[La(L4 )]3+ M-

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391

[La(L4 )]3+ isomerisation process on the NMR time scale. Compared to the parent complexes [La(L3 )3 ]3+ which display enantiotopic methylene protons for T > 233 K (see sect. 3.1.3), the introduction of the covalent TREN tripod in [La(L4)]3+ signiﬁcantly slows down the helical interconversion process. Protonation of the apical nitrogen atom produces the C3 -symmetrical podates [R(L4 +H)]4+ which display only marginally faster racemisation processes. Although some steric constraints induced by the tripod limit the thermodynamic stability of the podates [R(L4 )]3+ and [R(L4 +H)]4+ , stability constants conﬁrm their quantitative formation for a total ligand concentration of 0.05 mol · dm−3 and a stoichiometric ratio R: L4 = 1.0 (Renaud et al., 1999; ﬁg. 17). para para Plots of δij /Sz j vs Cj /Sz j (eq. (48)) and δij /Cj vs Sz j /Cj (eq. (49)) for 1 H and 13 C NMR data of [R(L4 )]3+ and [R(L4 +H)]4+ (R = Ce, Pr, Nd, Sm, Eu, Yb) show linear cor-

Fig. 17. Schematic formation of the C3 -symmetrical podates [R(L4 )]3+ and [R(L4 +H)]4+ in acetonitrile with numbering scheme. The representation of [R(L4 +H)]4+ corresponds to the crystal structure of [Eu(L4 +H)](CF3 SO3 )3 (PF6 )(CH3 CN)0.5 (Renaud et al., 1999).

392

C. PIGUET AND C.F.G.C. GERALDES

para

para

Fig. 18. Plots of (a) δij /Sz j vs Cj /Sz j (eq. (48)) and (b) δij /Cj vs Sz j /Cj (eq. (49)) for C5 in [R(L4 )]3+ (2) and [R(L4 +H)]4+ (P) (R = Ce–Eu, Yb, CD3 CN/CD3 NO2 (1:1), 298 K, redrawn from Renaud et al. (1999)). Table 7 Computed values for contact (Fi ), pseudo-contact (B02 Gi ) terms and agreement factors (AFi ) for 1 H- and 13 Cnuclei in the podates [R(L4 )]3+ and [R(L4 +H)]4+ (R = Ce–Eu, Yb, CD3 CN/CD3 NO2 (1:1), 298 K, Renaud et al. (1999)). See ﬁg. 17 for the atom-numbering scheme

Fi B02 Gi AFi Fi B02 Gi AFi

Fi B02 Gi AFi Fi B02 Gi AFi

H3 0.04(1) 0.016(6) 0.44 C1 0.09(8) 0.11(4) 0.54 H3 −0.01(1) −0.00(1) 0.97 C1 0.2(2) −0.41(9) 0.33

H4 0.13(4) −0.02(2) 0.36 C3 0.08(3) 0.01(2) 0.39

[R(L4 )]3+ H5 H6 0.10(4) 0.17(3) −0.03(2) 0.01(1) 0.46 0.27 C4 C5 3.4(4) −1.1(4) 0.2(2) −0.04(2) 0.18 0.06

H8 0.01(1) −0.002(3) 0.61 C6 3.2(3) 0.0(1) 0.15

H10 0.001(2) −0.004(7) 0.93 C8 −0.1(2) 0.002(7) 0.08

C10 −0.06(3) 0.01(1) 0.44

H4 0.08(7) 0.20(4) 0.31 C3 0.3(6) −0.04(3) 0.30

[R(L4 +H)]4+ H5 H6 0.04(5) 0.1(4) 0.13(2) 0.10(2) 0.31 0.31 C4 C5 2.8(2) −1.1(1) 0.4(1) 0.24(4) 0.15 0.11

H8 0.01(1) −0.024(4) 0.24 C6 3.0(2) 0.28(9) 0.12

H10 0.03(6) −0.2(3) 0.25 C8 −0.13(1) 0.00(1) 0.15

C10 −0.01(5) −0.16(2) 0.24

relations for all the paramagnetic lanthanides studied (ﬁg. 18). The separation of the contact and pseudo-contact contributions according to eq. (47) for each nuclei in the two complexes show very similar contact Fi terms, but signiﬁcantly different pseudo-contact B02 Gi terms which explains the different slopes obtained on ﬁg. 18a (table 7). Calculation of geometrical

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

393

factors Gi from the crystal structure of [Eu(L4 +H)]4+ combined with a detailed analysis of the sign of the B02 Gi terms in the two complexes suggest that the position of R(III) is slightly shifted toward the lone pair of the apical nitrogen in [R(L4 )]3+ , while R(III) is moved away from the apical site upon protonation in [R(L4 +H)]4+ . Although possible variations of B02 have not been considered by the authors, the existence of a single isostructural series for [R(L4 )]3+ and [R(L4 +H)]4+ strongly contrasts with the structural change assigned to the parent complexes [R(L3 )3 ]3+ . This peculiar behaviour of the podates has been ascribed to the improved structural control imposed by the rigid tripod (Renaud et al., 1999). The limited available set of paramagnetic shifts collected for [R(L4 )]3+ and [R(L4 +H)]4+ in the second part of the lanthanide series (R = Yb) prevents the application of the crystal-ﬁeld indepenj dent technique (eq. (51)), but attempts to estimate magnetic anisotropies χzz − (1/3) Tr χ j with eq. (58) give only poorly reliable results because, among the available 13 LIS for protons and carbons, the contact contributions of only three carbons C1, C8 and C10 can be neglected. 3.1.5. [RM(L5 )3 ]5/6+ (M = Zn, Co; L5 = 2-{6-[N ,N -diethylcarboxamido]-pyridin-2-yl} -1,1’-dimethyl-5,5’-methylene-2’-(5-methylpyridin-2-yl)bis(1H-benzimidazole) The use of unsymmetrical tridentate binding units for the complexation of nine-coordinate R(III) is strongly limited by the head-to-head-to-head (HHH) ↔ head-to-head-to-tail (HHT) isomerism resulting from the two different possible arrangements of the strands in [RL3 ] complexes. Covalent tripods are rarely used in this context because severe steric constraints often prevent the regular wrapping of the strands required for meridional tri-coordination (Renaud et al., 1999; Bretonnière et al., 2000; see sect. 3.1.4). Piguet et al. (1996) have taken advantage of the virtues of thermodynamic self-assembly for preparing pure d-f heterobimetallic complexes in which threefold symmetry (i.e., a strict HHH arrangement of the tridentate binding units) results from the use of a ﬂexible non-covalent tripod. The segmental ligand L5 has been designed for this purpose since it possesses a NN bidentate binding unit coded for the coordination of soft d-block ions and an unsymmetrical NNO tridentate binding unit coded for the coordination of 4f-block ions (Piguet et al., 2000). Upon stoichiometric mixing of L5 (3 eq.) with Zn(II) (1 eq.) and R(III) (1 eq.) in acetonitrile, the C3 -symmetrical triple-stranded helicates (HHH)-[RZn(L5)3 ]5+ are quantitatively formed for total ligand concentrations larger than 10−4 mol · dm−3 (ﬁg. 19). In these systems, the d-block ions is pseudo-octahedrally sixcoordinated by the three bidentate binding unit, thus providing a non-covalent tripod which organizes the helical wrapping of the three tridentate chelates for their coordination to the pseudo-tricapped trigonal prismatic lanthanides. When diamagnetic Zn(II) is introduced into the non-covalent tripod, R(III) is the only source of paramagnetism and the paramagnetic NMR data can be analyzed with the usual model-free methods. As a result of (i) the tight wrapping of the three ligand strands in (HHH)[RZn(L5)3 ]5+ and (ii) the strong metal–ligand interactions associated with multiple interactions (Prins et al., 2001; Swiegers and Malefetse, 2001), the dynamic interconversion between the helical enantiomers P P -[RZn(L5 )3 ]5+ MM-[RZn(L5)3 ]5+ is blocked on the NMR time scale in the temperature range accessible in acetonitrile (233–343 K). All methylene protons remain diastereotopic and the 1 H NMR spectra reﬂect the quantitative formation of

394

C. PIGUET AND C.F.G.C. GERALDES

Fig. 19. Self-assembly of L5 with LaIII and ZnII in acetonitrile. The stability constant for each deﬁned equilibrium is given as log(K). The representation of [LaZn(L5 )3 ]5+ corresponds to the crystal structure of [EuZn(L5 )3 ](CF3 SO3 )3 (ClO4 )(CH3 CN)4 (Piguet et al., 1996).

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

395

para

Fig. 20. Plots of δij /Sz j vs Cj /Sz j (eq. (48)) for H13 in [RZn(L5 )3 ]5+ (R = Ce, Pr, Nd, Eu, Tm, Yb, 298 K, drawn from data reported by Piguet et al. (1996)). Table 8 Computed values for contact (Fi ), pseudo-contact (B02 Gi ) terms and agreement factors (AFi ) for 1 H-nuclei in the complexes [RZn(L5 )3 ]5+ (R = Ce, Pr, Nd, Eu, Tm, Yb, CD3 CN, 298 K, Piguet et al. (1996)). See ﬁg. 19 for the atom-numbering scheme

Fi B02 Gi AFi

Me1 −0.015 0.037 0.13

Me2 −0.018 0.055 0.13

Bidentate binding unit H1 H2 H3 −0.029 −0.020 −0.024 0.067 0.038 0.061 0.12 0.10 0.11

H4 −0.029 0.051 0.09

H5 −0.022 0.030 0.08

H6 −0.105 0.0304 0.14

Tridentate binding unit Me3 H9 H10 H11 H12 H13 H14 H17 H18 H19 H20 Fi 0.060 −0.248 −0.03 0.143 0.335 0.178 0.337 0.144 −0.003 −0.039 −0.255 B02 Gi −0.202 0.903 0.017 −0.078 −0.250 −0.207 −0.242 −0.118 −0.030 0.057 0.737 AFi 0.17 0.15 0.27 0.09 0.11 0.09 0.10 0.10 0.14 0.11 0.14

the C3 -symmetrical complexes [RZn(L5)3 ]5+ (R = La, Ce, Pr, Nd, Sm, Eu, Tm, Yb, Lu) para in solution (Piguet et al., 1996). Although plots of δij /Sz j vs Cj /Sz j (eq. (48)) and para δij /Cj vs Sz j /Cj (eq. (49)) for 1 H NMR data suggest that R = Tm, Yb do not belong to the straight line found for R = Ce–Eu (ﬁg. 20), multi-linear least-squares ﬁts of eq. (47) considering a single isostructural series (R = Ce–Yb) have been applied for the separation of contact and pseudo-contact contributions (Fi and B02 Gi terms are collected in table 8). It is thus not surprising that only poor agreement factors AFi are obtained, but the triplestranded helical complex possesses enough protons with negligible contact contributions to j allow reliable calculations of the magnetic anisotropies χzz − (1/3) Tr χ j for each studied lanthanide (eq. (58)). Among twelve available aromatic protons, six are connected to the bidentate binding unit and exhibit no contact contribution. Multi-linear 12 × 6 ﬁts using the geometj rical factors Gi obtained from the crystal structure of [EuZn(L5)3 ]5+ give χzz − (1/3) Tr χ j values for R = Ce, Pr, Nd, Eu, Tm, Yb which are in qualitative good agreement with Bleaney’s Cj factors (Piguet et al., 1996). It was concluded that (i) the crystal structure of [EuZn(L5)3 ]5+ is a satisfying structural model for the complete lanthanide series and (ii) helication of the strands and coordination to d-block ions ensures a rigid and well-deﬁned coordination site for

396

C. PIGUET AND C.F.G.C. GERALDES

Fig. 21. Self-assembly of (HHH)-[RCoII (L5 )3 ]5+ followed by oxidation (post-modiﬁcation) to give (HHH)-[RCoIII (L5 )3 ]6+ . The representation of [RCo(L5 )3 ]6+ corresponds to the crystal structure of [LaCo(L5 )3 ](ClO4 )5.5 (OH)0.5 (CH3 CN)4 (H2 O)2 (adapted from Rigault et al. (1998)).

R(III). The latter point has been exploited for investigating possible variations of crystal-ﬁeld parameters within isostructural series of rigid complexes. In order to design highly rigid helicates programmed for displaying a single isostructural series in solution, the kinetically inert diamagnetic Co(III) (d6 low spin) has been introduced into the non-covalent tripod by using a self-assembly process with oxidative post-modiﬁcation (Rigault et al., 1998; ﬁg. 21). No decomplexation occurs in acetonitrile (10−1 –10−5 mol · dm−3 ) and the almost identical crystal structures obtained for lanthanide ions of extreme sizes (HHH)-[RCo(L5)3 ]6+ (R = La, Lu) strongly suggest that the considerable rigidity of the wrapped ligand strands minimizes structural variations associated with the lanthanide contraction (ﬁg. 22, Rigault et al. (2000b)). The 1 H NMR spectra of (HHH)-[RCo(L5)3 ]6+ (R = La–Lu, except Pm, Gd) conﬁrm the quantitative formation of rigid C3 -symmetrical complexes displaying systematic diastereotopic methylene protons between 233–343 K in acetonitrile. Field-dependent T1 and T2 relaxation measurements for (HHH)-[RCo(L5)3 ]6+ (R = Tb, Tm) ﬁtted with eq. (15) (ﬁg. 23a) and eq. (16) (ﬁg. 23b) respectively give R–Hi distances very close to those found in the solid state in agreement with negligible structural changes occurring along the lanthanide series in solution (Rigault et al., 2000b). j Magnetic anisotropies χzz − (1/3) Tr χ j for R = Ce–Yb except Pm, Gd (0.002 AFj 0.06, table 9) have been computed with eq. (58) and using ﬁve contact contributions δijc (i = H9, H11–H14) and the geometrical Gi factors obtained from the crystal structures of (HHH)-[RCo(L5)3 ]6+ (R = La, Lu). A qualitative good agreement (AF = 0.23) is obtained between the experimental magnetic anisotropies (scaled to −100 for Dy(III) and corrected for the variation of the crystal-ﬁeld parameter near the middle of the series (vide supra), table 9) and Bleaney’s factors (table 3). Further non-linear least-squares reﬁnements of the molecular

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

397

Fig. 22. Perspective views of (a) (HHH)-[LaCoIII (L5 )3 ]6+ and (b) (HHH)-[LuCoIII (L5 )3 ]6+ perpendicular to the pseudo-C3 axis in the crystal structures of [LaCo(L5 )3 ](ClO4 )5.5 (OH)0.5 (CH3 CN)4 (H2 O)2 and [LuCo(L5 )3 ](CF3 SO3 )6 (H2 O)(CH3 CN)2 (adapted from Rigault et al. (2000b)).

para

para

Fig. 23. Plot of (a) 1/T1i vs (H02 /(1 + ω2 τr2 )) (eq. (15)) and 1/T2i vs H02 (eq. (16)) for H12 in (HHH)[TbCoIII (L5 )]6+ (acetonitrile, 298 K, redrawn from Rigault et al. (2000b)).

structure using the crystal structure of (HHH)-[LuCo(L5)3 ]6+ as the initial model and simultaj neously varying the axial coordinates θi and ri and χzz − (1/3) Tr χ j (the contact contribution for H9, H11–H14 are ﬁxed and calculated from the Fi terms of table 10: δijc = Fi Sz j ) show only minor changes for minimizing the square of the error between calculated and experimental pseudo-contact shifts. However, the ﬁnal agreement of the computed magnetic anisotropies (corrected for the variation of the crystal-ﬁeld parameter) and Bleaney’s factors slightly improves (AF = 0.20). Rigault et al. (2000b) conclude that no signiﬁcant structural change

398

C. PIGUET AND C.F.G.C. GERALDES

Table 9 Axial magnetic anisotropies for (HHH)-[RCon (L5 )3 ](3+n)+ (n = 2, 3) in acetonitrile (Rigault et al., 2000b)a (HHH)-[RCoIII (L5 )3 ]6+ j χzz − (1/3) Tr χ j /ppm·Å3

Ce Pr Nd Eu Tb Dy Ho Er Tm Yb

413(10) 666(13) 300(8) −342(9) 4518(92) 4941(150) 2660(44) −562(18) −1614(44) −651(19)

Scaled Cj b −5.2(1) −8.0(2) −3.8(1) 4.3(1) −91(2) −100(3) −53(1) 11.4(4) 32.7(9) 13.2(4)

(HHH)-[RCoII (L5 )3 ]5+ j χzz − (1/3) Tr χ j /ppm·Å3

597(185) 866(196) 501(131) −532(169) 5330(126) 5668(189) 3258(143) −664(113) −2107(54) −764(81)

Scaled Cj b −6(2) −10(2) −5.5(1.4) 6(2) −94(3) −100(3) −57(3) 12(2) 37(1) 13(2)

a Values corrected for crystal-ﬁeld effects. b Ratios relative to C Dy = −100.

occurs along the lanthanide series and that both crystal structures ((HHH)-[RCo(L5)3 ]6+ , R = La, Lu) are satisfying structural models. The analyses of the 1 H-NMR data with the crystal-ﬁeld independent technique (eq. (51)) para para display straight lines for plots of δij /Sz j vs δkj /Sz j in complete agreement with isostructurality along the complete lanthanide series and no signiﬁcant change of the Gi factors (ﬁg. 24). para para Plots of δij /Sz j vs Cj /Sz j (eq. (48)) and δij /Cj vs Sz j /Cj (eq. (49)) using crystal-ﬁeld dependent techniques show systematic abrupt breaks near the middle of the lanthanide series (between R = Eu and R = Tb) which imply a concomitant change of the contact Fi and pseudo-contact B02 Gi terms (table 10, ﬁg. 25). Since Gi is essentially invariant, an abrupt variation of the crystal-ﬁeld parameter B02 is required to rationalize the NMR data.

Fig. 24. Crystal-ﬁeld independent plot of para para δij /Sz j vs δkj /Sz j (eq. (51)) for the H9–H12 pair in (HHH)-[RCoIII (L5 )3 ]6+ (R = Ce–Yb, acetonitrile, 298 K, redrawn from Rigault and Piguet (2000)).

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

399

Table 10 Computed values for contact (Fi ), pseudo-contact (B02 Gi ) terms for 1 H nuclei in the complexes (HHH)[RCoIII (L5 )3 ]6+ and (HHH)-[RCoII (L5 )3 ]5+ (R = Ce–Eu and R = Tb–Yb, CD3 CN, 298 K, Rigault et al. (2000b)). See ﬁg. 19 for the atom-numbering scheme Compd [R CoIII (L5 )3 ]6+ R = Ce–Eu [R CoIII (L5 )3 ]6+ R = Tb–Yb [R CoII (L5 )3 ]5+ R = Ce–Eu [R CoII (L5 )3 ]5+ R = Tb–Yb

Compd

Fi B02 Gi Fi B02 Gi Fi B02 Gi Fi B02 Gi

Me1

Me2

−0.01(1) 0.035(3) 0.03(1) 0.021(1) 0.07(2) 0.08(2) 0.03(1) 0.026(3)

−0.01(1) 0.060(3) 0.05(1) 0.038(1) −0.01(1) 0.027(6) 0.03(1) 0.044(2)

H9

[R CoIII (L5 )3 ]6+ R = Ce–Eu [R CoIII (L5 )3 ]6+ R = Tb–Yb [R CoII (L5 )3 ]5+ R = Ce–Eu [R CoII (L5 )3 ]5+ R = Tb–Yb

Fi −0.07(3) B02 Gi 0.93(3) Fi 0.79(4) B02 Gi 0.58(1) Fi −0.11(5) B02 Gi 0.94(4) Fi 0.76(7) B02 Gi 0.64(2)

H10

Bidentate binding unit H1 H2 −0.01(1) −0.01(1) 0.071(3) 0.038(1) 0.06(1) 0.03(1) 0.045(5) 0.024(1) 0(0) 0.01(1) 0(0) 0.022(5) 0.05(1) 0.026(5) 0.050(3) 0.030(2)

H3

H4

H5

H6

−0.01(1) 0.058(2) 0.05(1) 0.036(1) 0.07(5) −0.10(4) −0.01(2) 0.053(6)

−0.01(1) 0.068(1) 0.05(1) 0.046(1) 0.02(2) 0.01(2) 0.02(1) 0.051(3)

−0.01(1) 0.060(1) 0.04(1) 0.043(3) −0.02(1) 0.058(6) 0.04(1) 0.037(2)

−0.05(1) 0.29(1) 0.22(2) 0.177(1) −0.15(7) 0.48(6) 0.30(5) 0.20(2)

Tridentate binding unit H11 H12 H13

−0.01(1) 0.12(1) 0.24(1) 0.067(4) −0.019(6) −0.33(1) 0.06(1) 0.09(1) −0.11(3) 0.038(2) −0.007(3) −0.20(1) −0.03(1) 0.10(1) 0.24(2) 0.080(7) 0.001(6) −0.35(1) 0.05(1) 0.10(1) 0.02(1) 0.041(2) −0.001(2) −0.276(5)

0.09(2) −0.23(1) 0.06(2) −0.132(8) 0.09(2) −0.24(2) 0.08(3) −0.20(1)

H14

Me3

Me4

Me5

0.17(1) −0.15(1) −0.02(3) −0.097(9) 0.17(1) −0.16(1) 0.06(3) −0.133(9)

0.00(1) −0.149(2) −0.16(1) −0.096(5) −0.06(2) −0.16(1) −0.16(2) −0.109(6)

−0.02(2) 0.33(2) 0.29(3) 0.20(1) 0.02(2) −0.11(2) −0.06(2) −0.038(6)

0.00(2) −0.09(2) −0.04(2) −0.041(7) −0.06(3) 0.38(3) 0.31(4) 0.24(1)

para

Fig. 25. Plots of δij /Sz j vs Cj /Sz j (eq. (48)) for H10 in (HHH)-[RCoIII (L5 )3 ]6+ (") and (HHH)-[RCoII (L5 )3 ]5+ (F) (R = Ce– Yb, acetonitrile, 298 K, redrawn from Rigault et al. (2000b)).

A plot of B02 Gi (R = Ce–Eu) vs B02 Gi (R = Tb–Yb) gives a straight line whose slope corresponds to the ratio of the crystal-ﬁeld parameters B02 (R = Ce–Eu) B02 (R = Tb–Yb)

= 1.6(2)

400

C. PIGUET AND C.F.G.C. GERALDES

(Rigault and Piguet, 2000). The decrease of B02 with the lanthanide contraction matches the expected reduced interaction between metal-centred 4f and ligand donor orbitals. The observation of an abrupt change in the crystal-ﬁeld parameters near the middle of the lanthanide series, sometimes referred to as the ‘gadolinium break’ is reminiscent of related changes established for Bqk in crystals of Na3 [R(L1 –2H)3]·2NaClO4 ·6H2 O (Hopkins et al., 1998; Görller-Walrand and Binnemans, 1996; Rigault and Piguet, 2000; ﬁg. 9). For six-rank parameters (k = 6), the remarkable discontinuity between the ﬁrst and second half of the lanthanide series is an indication for the need to include two-electron operators in the crystal-ﬁeld Hamiltonian (Judd, 1979), but its origin remains obscure for second-rank parameters (GörllerWalrand and Binnemans, 1996; Rigault and Piguet, 2000). It is difﬁcult to simply assign this abrupt variation of the B02 parameters to deviation from Bleaney’s approach, because the experimental magnetic anisotropies determined for (HHH)-[RCo(L5)3 ]6+ satisfyingly match the Cj factors, a strong support for limiting the T −n series to the second-order term. Surprisingly, the concomitant change of the contact term Fi observed according to eqs. (48), (49) (table 10) has negligible effects on the intercept Fi − Fk Rik of linear plots obtained according to eq. (51) (ﬁg. 24). Speciﬁc compensation effects have been demonstrated for (HHH)[RCo(L5 )3 ]6+ (Rigault et al., 2000b), but variations of Fi terms are expected to produce two para para parallel straight lines for δij /Sz j vs δkj /Sz j as demonstrated for the cryptate [R(L6)]3+ (see sect. 3.1.6, Platas et al. (1999)). Reduction of Co(III) into Co(II) provides a second fast-relaxing paramagnetic centre (Co(II), d7 high spin, S = 3/2) within the triple-stranded helicates (HHH)-[RCo(L5)3 ]5+ and this strongly affects the 1 H-NMR spectra. Since no intermetallic R-Co(II) magnetic coupling can be detected at 298 K, the paramagnetic shifts induced by the two metallic centres are additive and eq. (59) holds if no major structural change occurs between (HHH)-[RCoII (L5 )3 ]5+ and (HHH)-[RCoIII(L5 )3 ]6+ (Rigault et al., 2000b) para

para

δij (RCo(II)) = δi

para

(LaCo(II)) + δij (RCo(III)).

(59)

Satisfying predictions for the NMR spectra of (HHH)-[RCoII (L5 )3 ]5+ are obtained which allow the complete assignment of the 1 H NMR signals in strongly paramagnetic lanthanidecontaining complexes. Detailed model-free analyses (eqs. (48), (49), (51)) using the complex (HHH)-[LaCoII(L5 )3 ]5+ as the ‘diamagnetic’ reference (eq. (3)), evidence very similar structural properties for (HHH)-[RCoII (L5 )3 ]5+ and (HHH)-[RCoIII (L5 )3 ]6+ despite the relative 36% increase of the ionic radius when going from Co(III) (d6 low spin) to Co(II) (d7 high spin, Shannon (1976)). As far as paramagnetic lanthanide induced shifts are concerned, a closely related concomitant abrupt change of the hyperﬁne constants (via Fi ) and of the crystal-ﬁeld parameter B02 (R = Ce–Eu) B02 (R = Tb–Yb)

= 1.6(3)

is observed for (HHH)-[RCoII(L5 )3 ]5+ (table 10, ﬁg. 25), together with comparable magnetic anisotropies (table 9). Rigault et al. (2000b) conclude that the triple-stranded helicates are rigid enough to maintain very similar solution structures when the size of the f- and d-block

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

401

ions is varied within an acceptable range. However, the one-nucleus crystal-ﬁeld dependent methods (eqs. (48), (49)) cannot be used for detecting structural changes because of unpredictable abrupt variations of the crystal-ﬁeld parameter along the lanthanide series. The twonuclei crystal-ﬁeld independent technique (eq. (51)) should be preferred and systematically applied when using model-free analyses. 3.1.6. [R(L6 )]3+ (L6 = azacryptand, see ﬁg. 26) The capping of both termini of three tridentate chelating units with covalent tripods provides highly rigid macrobicyclic receptors (i.e., cryptands), which are ideally suited for investigating variations of crystal-ﬁeld parameters within isostructural series. Platas et al. (1999) have iso-

Fig. 26. Template formation of the C3 -symmetrical cryptates [R(L6 )]3+ in water with numbering scheme. The representation of [R(L6 )(NO3 )]2+ corresponds to the crystal structure of [Eu(L6 )(NO3 )](NO3 )2 (H2 O)4 (Platas et al., 1999).

402

C. PIGUET AND C.F.G.C. GERALDES

lated the monometallic cryptates [R(L6 )(NO3 )](NO3 )2 from the one-pot template reaction of tris(2-aminoethyl)amine (TREN) tripods with tridentate 2,6-diformyl-4-methylphenol in the presence of R(NO3 )3 . Crystal structures of [R(L6 )(NO3 )](NO3)2 (R = Ce, Nd, Eu, Y) show the formation of pseudo-trigonal complexes in which the lanthanide is placed asymmetrically at one end of the cavity, the four nitrogen atoms of one TREN tripod, three oxygen of the protonated phenols and two oxygen atoms of a bidentate nitrate ensuring nine-coordination (ﬁg. 26). No major structural change is observed in the solid state for a relative lanthanide contraction of 11% (i.e., Y(III) displays an ionic radius comparable to that of Ho(III), Shannon (1976)), but threefold symmetry is removed by the coordination of the nitrate counter-anion. Dissolution of the complexes in D2 O (5·10−3 mol · dm−3 , pD = 5.8, 298 K) provides strict C3 -symmetry on the NMR time scale in line with decomplexation of the nitrate anion or fast on-off exchange mechanisms. Since no decomplexation of the macrobicyle occurs under these conditions, relaxation and hyperﬁne NMR shifts have been collected at a single concentration. Dynamic intramolecular δ λ conformational interconversion of the ﬁve-membered chelate rings rapidly exchange H2axial with H2equatorial on the NMR time scale. A detailed Eyring analysis of the line shape for [La(L6)]3+ gives G= = 70(3) kJ/mol at 298 K, a kinetics barrier comparable to that found for the same conformational interconversion occurring in para [La(L10–4H)]− (60.7 kJ/mol, see sect. 3.2.2). Plots of δij /Sz j vs Cj /Sz j (eq. (48)) para and δij /Cj vs Sz j Cj (eq. (49)) for 1 H NMR data of [R(L6)3 ]3+ (R = Ce–Yb, except Pm, Gd) display an abrupt deviation from linearity between R = Eu and R = Tb and require two different straight lines (ﬁg. 27). Two different isostructural series are considered for R = Ce–Tb and Er–Yb, and two sets of contact Fi and pseudo-contact B02 Gi terms are obtained according to least-squares ﬁts of eq. (47) (table 11, Platas et al. (1999)). The simultaneous least-squares ﬁts of lanthanide induced relaxation (LIR, T1 ) according to eq. (18) and lanthanide induced shifts (LIS) according to eq. (47) with the crystal structures of [R(L6 )(NO3)](NO3 )2 as starting molecular models display only minor shift of R(III) from its original location. For the lighter lanthanides (R = Ce–Eu), the best ﬁt shows a slight shift

para

para

Fig. 27. Plots of (a) δij /Sz j vs Cj /Sz j (eq. (48)) and (b) δij /Cj vs Sz j /Cj (eq. (49)) for H3 in [R(L6 )]3+ (R = Ce–Yb, D2 O, 298 K, adapted from Platas et al. (1999)).

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

403

Table 11 Computed values for contact (Fi ), pseudo-contact (B02 Gi ) terms for 1 H-nuclei in the complexes [R(L6 )]3+ (R = Ce– Yb, D2 O, 298 K, Platas et al. (1999)). See ﬁg. 26 for the atom-numbering scheme Series R = Ce–Eu Fi B02 Gi

H1ax

H1eq

H2ax

H2eq

H3

H4

H5

1.81(28)

1.30(25)

0.55(13)

0.4(1)

3.48(6)

0.25(4)

0.01(2)

−2.05(22)

−1.78(15)

−0.01(4)

1.03(5)

0.49(4)

0.18(1)

H6

H7

H8eq

H9ax

H9eq

−0.06(4) H8ax

Fi

0.21(1)

0.06(1)

0.15(6)

0.11(6)

0.21(6)

0.65(6)

B02 Gi

0.13(1)

−0.13(1)

−0.75(5)

−0.50(7)

−0.54(6)

−0.44(7)

H1ax

H1eq

H2ax

H2eq

H3

H4

0.33(32)

0.42(34)

0.79(13)

0.33(5)

0.57(17)

0.40(15)

Series R = Tb–Yb Fi B02 Gi

−1.06(9)

−0.95(11)

−0.09(5)

−0.05(2)

0.52(5)

0.55(5)

H6

H7

H8ax

H8eq

H9ax

H9eq

a

a

a

a

a

a

a

a

a

a

a

a

Fi B02 Gi

H5 −0.11(1) 0.06(1)

a Not determined.

of R(III) toward the apical nitrogen atom of the TREN tripod (0.3 Å) and an angle of 5◦ between the principal magnetic z axis and the R–Napical vector (0◦ is expected for an axial system). Similar results are obtained for the heavy lanthanides R = Tb–Yb except for a strict alignment of the magnetic z axis and the R–Napical direction. Platas et al. (1999) conclude that the cryptates [R(L6 )3 ]3+ are rigid in solution and no major structural change occurs in solution near the middle of the series. The break observed according to eqs. (48), (49) is thus assigned to a concomitant variation of Fi and B02 as similarly suggested for (HHH)[RCo(L5 )3 ]6+ (see sect. 3.1.5). The application of the crystal-ﬁeld independent technique (eq. (51)) supports this statement and two parallel straight lines corresponding to the R = Ce– para para Eu and R = Tb–Yb series are observed for plots of δij /Sz j vs δkj /Sz j (ﬁg. 28). Since the slopes correspond to Rik = Gi /Gk , no structural change occurs near the middle of the lanthanide series, but the variations of the hyperﬁne constants result in different intercepts Fi − Fk Rik . Finally, a plot of B02 Gi (R = Ce–Eu) vs B02 Gi (R = Tb–Yb) gives a straight line whose slope corresponds to the ratio of the crystal-ﬁeld parameters B02 (R = Ce–Eu) B02 (R = Tb–Yb)

= 1.9(1).

The strict analogy between the behaviours of the rigid helicates (HHH)-[RCo(L5)3 ]5/6+ and the cryptates [R(L6)]3+ strongly suggest that the ‘gadolinium break’ effect is a common trend when analysing paramagnetic NMR data (Rigault and Piguet, 2000).

404

C. PIGUET AND C.F.G.C. GERALDES

Fig. 28. Crystal-ﬁeld independent para para plot of δij /Sz j vs δkj /Sz j (eq. (51)) for the H1–H3 pair in [R(L6 )]3+ (R = Ce–Yb, D2 O, 298 K, adapted from Platas et al. (1999)). para

para

para

para

Finally, plots of δij /δkj vs δlj /δkj according to the three-nuclei method (eq. (53)) conﬁrm the break occurring near the middle of the series and the experimental slopes (Sik − Rik ) (Slk − Rlk ) and intercepts (Slk Rik − Sik Rlk ) (Slk − Rlk ) can be satisfactorily predicted from Fi terms obtained with eqs. (48), (49) and Rik terms obtained with eq. (51) (ﬁg. 29, Geraldes et al. (2001)). 3.1.7. [R(L7 –2H)3 ]3− (L7 = 2,6-pyridinedicarboxylic acid and derivatives) According to the systematic observation of abrupt variations of the second-rank crystalﬁeld parameter near the middle of the lanthanide series in rigid threefold complexes on one side (see sects. 3.1.5 and 3.1.6) and the structural change evidenced in [R(L3 )3 ]3+ between R = Tb and R = Er on the other side (see sect. 3.1.3), the strict isostructurality combined with the invariance of B02 proposed by Donato and Martin (1972) and Reilley et al. (1975) for the closely related complexes [R(L7 –2H)3 ]3− in D2 O become suspicious and deserve to be re-examined. As discussed for [R(L1 –2H)n ](3−2n)+ (n = 1, 2, 3, see sect. 3.1.1), the thermodynamic properties of [R(L7 –2H)n ](3−2n)+ (n = 1, 2, 3) have been extensively studied by Grenthe (1961) leading to calculated ligand speciations of [R(L7 – 2H)3 ]3− (95%), [R(L7 –2H)2(OH2 )3 ]− (3%) and [L7 –2H]2− (2%) for a total ligand concentration of 0.03 mol · dm−3 and a stoichiometric ratio R/L7 = 0.33 (water, pH = 6, 298 K). In excess of ligand (R/L7 = 0.25), fast intermolecular ligand-exchange processes on the NMR time scale are detected for [La(L7–2H)3 ]3− (D2 O, 283–353 K), while the stronger R-ligand

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

para

405

para

para

para

Fig. 29. Plot of δij /δkj vs δlj /δkj according to the three-nuclei method (eq. (53)) for the triad H2ax –H3–H5 in [R(L6 )]3+ (R = Ce–Yb, D2 O, 298 K, redrawn from Geraldes et al. (2001)).

dative bonds with smaller rare earth ions (R = Y, Lu) provide distinct 1 H NMR signals at 283 K for free and complexed ligands (Alsaadi et al., 1980a). Ouali et al. (2002) have obtained G= ([Y(L7–2H)3 ]3− ) = 68(1) and G= ([Lu(L7–2H)3 ]3− ) = 74(1) kJ/mol at the coalescence temperatures (318 and 348 K respectively) for this intermolecular ligand-exchange process together with a smaller value G= ([La(L7–2H)3 ]3− ) 59 kJ/mol in agreement with the original trend proposed by Peters (1988) for the closely related oxydiacetate complexes [R(L1 –2H)3 ]3− . However, the equilibrium quantities of [R(L7 –2H)2(OH2 )3 ]− and [L7 –2H]2− are small enough to be neglected for NMR measurements obtained at high concentration and for R/L7 = 0.33 (Pons and Millet, 2001). The observed 1 H and 13 C NMR data conﬁrm the formation of D3 -symmetrical triple-helical complexes [R(L7 –2H)3 ]3− and [R(L7a –2H)3 ]3− in solution (Reilley et al., 1975) in agreement with the numerous solidstate crystal structures reported for (cation)3[R(L7 –2H)3] along the complete lanthanide series which show R(III) in pseudo-tricapped trigonal prismatic sites, six oxygen atoms of the carboxylate groups occupying the vertices of the trigonal prism and the three nitrogen atoms of the pyridine rings capping the rectangular faces (Hopkins et al., 1996; Harrowﬁeld et al., 1995; ﬁg. 30). The introduction of diastereotopic probes in [R(L7b–2H)3 ]3− shows two separated 1 H NMR signals for the methylene protons for R = Eu, Tm and Yb which coalesce around 298 K (Ouali et al., 2002). The associated free energies of activation G= ([Eu(L7b– 2H)3 ]3− ) = 63(1) kJ/mol, G= ([Tm(L7b–2H)3 ]3− ) = 64(1) kJ/mol and G= ([Yb(L7b– 2H)3 ]3− ) = 60(1) kJ/mol point to a minor dependence of the racemisation process P [R(L7b –2H)3 ]3− M-[R(L7b–2H)3 ]3− on the size of R(III) as similarly observed by Peters (1988) for [R(L1 –2H)3 ]3− . The ﬁrst-order rate constants for the ground-state helical racemi298 K = 50–200 s−1 ) are in good agreement with those obtained in the exsation process (krac cited state by polarized luminescence for [R(L7 –2H)3 ]3− (R = Eu, Tb, Huskowska and Riehl (1995)). Finally, 1 H relaxation measurements (Alsaadi et al., 1980b) and time-resolved luminescence (An et al., 2000) for [R(L7 –2H)3 ]3− demonstrate that no water molecule interacts

406

C. PIGUET AND C.F.G.C. GERALDES

Fig. 30. Schematic formation of the D3 -symmetrical complexes [R(L7 –2H)3 ]3− in water with numbering scheme. The representation of [R(L7 –2H)3 ]3− corresponds to the crystal structure of [Cr(sarcophagine)][La(L7 –2H)](H2 O)8 (Harrowﬁeld et al., 1995).

with R(III) in the ﬁrst coordination sphere along the complete lanthanide series, thus leadpara ing to well-deﬁned D3 -symmetrical triple helices in solution. Original plots of δij /Sz j para vs Cj /Sz j (eq. (48)) and δij /Cj vs Sz j /Cj (eq. (49)) for 1 H and 13 C NMR data of [R(L7 –2H)3 ]3− (R = Pr, Eu, Tb–Yb) reported by Reilley et al. (1975, 1976) suggested linear behaviours compatible with isostructurality (i.e., invariance of Gi ) and invariances of Fi and B02 along the complete lanthanide series. Moreover, least-squares ﬁts of the molecular structure based on Gi calculated for the crystal structures of (cation)3[R(L7–2H)3 ] showed only minor variations between solid-state and solution structures. Similar conclusions have been proposed by Platas-Iglesias et al. (2001) for 1 H NMR data of [R(L7c –2H)3 ]3− (R = Nd, Eu, Tb–Yb) except that the existence of a single isostructural series is further supported by linear correlations obtained with the crystal-ﬁeld independent technique (eq. (51), ﬁg. 31a), and minor variations of Fi between R = Dy and R = Ho are detected according the one-nucleus techniques (eqs. (48), (49), ﬁg. 31b). In both model-free analyses of [R(L7 –2H)3 ]3− (Reilley et al., 1975) and [R(L7c –2H)3 ]3− (Platas-Iglesias et al., 2001), only two members of the ﬁrst part of the lanthanide series are considered (R = Pr, Eu for Reilley et al. (1975) and R = Nd, Eu for Platas-Iglesias et al. (2001)), which strongly limits detection of breaks between light and heavy lanthanides according to eqs. (48), (49) and (51). Moreover, these reports contrast with the signiﬁcant variapc pc tions of the ratio of pseudo-contact contributions δH2j /δH3j noticed by Alsaadi et al. (1980a) between light and heavy lanthanides in their original treatment of NMR data collected for [R(L7 –2H)n ](3−2n)+ (n = 1, 2, 3) at different stoichiometric ratios. A new complete set of 1 H and 13 C NMR data for [R(L7 –2H) ]3− (R = Ce–Yb, except Pm, Gd, 298 K, pD = 6.0, 3 300 MHz) has been collected by Ouali et al. (2002) and analyzed with eqs. (48), (49), (51). para para Plots of δij /Sz j vs δkj /Sz j (eq. (51)) systematically display two different straight lines

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

para

407

para

Fig. 31. (a) Crystal-ﬁeld independent plot of δij /Sz j vs δkj /Sz j (eq. (51)) for the H5–H6 pair and (b) plot of para δij /Sz j vs Cj /Sz j for H6 in [R(L7c –2H)3 ]3− (R = Nd, Eu, Tb–Yb, D2 O, 298 K, redrawn from Platas-Iglesias et al. (2001)).

para

Fig. 32. Crystal-ﬁeld independent plot of δij /Sz j para vs δkj /Sz j (eq. (51)) for the H2–C2 pair in [R(L7 – 2H)3 ]3− (R = Ce–Yb, D2 O, 298 K, redrawn from Ouali et al. (2002)).

for R = Ce–Eu and R = Tb–Yb (ﬁg. 32) in contrast with the original treatment of Reilley et al. (1975), but in line with the observation of Alsaadi et al. (1980a). Two different isostructural series are observed and the Rik terms calculated from the crystal structures of [R(L7 – 2H)3 ]3− (R = La, Lu, Harrowﬁeld et al. (1995)) compare well with those found in solution for R = Tb–Yb, but not for R = Ce–Eu (table 12). Extensive molecular modeling shows that the latter Rik terms result from oscillations of the central pyridine rings displaying considerable amplitude for light R(III) (|α(O–C4–C1–N)| 46◦ , ﬁg. 33). For R = Tb–Yb, the stronger R–Npyridine bonds limit oscillations and only minor displacements from the equilibrium position can be detected. Although related distortions are not observed in the crystal structures of [R(L7 –2H)3 ]3− (R = La, Lu), large torsions of the pyridine rings are exempliﬁed in the

408

C. PIGUET AND C.F.G.C. GERALDES

Fig. 33. Oscillations of the pyridine rings in the complexes of [R(L7 –2H)3 ]3− with large lanthanides (R = Ce–Eu, adapted from Ouali et al. (2002)).

Table 12 para para Minimal set of geometric ratio Rik = Gi /Gk obtained from plots of δij /Sz j vs δkj /Sz j according to eq. (51) for [R(L7 –2H)3 ]3− (D2 O, 298 K, pD = 6, Ouali et al. (2002)).a See ﬁg. 30 for the atom-numbering scheme Rik Rik Rik Rik

(Ce–Eu)b (Tb–Yb)c ([La(L7 –2H)3 ]3− )d ([Lu(L7 –2H)3 ]3− )d

H2–H3 0.98(4) 1.15(1) 1.13 1.11

H2–C1 0.23(1) 0.20(1) 0.22 0.21

H2–C2 0.28(3) 0.60(2) 0.53 0.51

H2–C3 0.36(4) 0.64(2) 0.65 0.63

H2–C4 1(1) 1(5) 1.22 2.66

a A complete set of R data can be generated according to R = R · R . Errors obtained according to multilinear ik ik im mk least-squares ﬁts are given between parentheses. b Values for the ﬁrst isostructural series (Sm has been removed because of its faint paramagnetism). c Values for the second isostructural series. d Calculated for the crystal structures of [Cr(sarcophagine)][R(L7 –2H) ] after averaging to D -symmetry. 3 3

crystal structure of the analogous complex [La(L3)3 ]3+ (26.8◦ |α(O–C4–C1–N)| 43.8◦ , Renaud et al. (1997)). para para Plots of δij /Sz j vs Cj /Sz j (eq. (48)) and δij /Cj vs Sz j /Cj (eq. (49)) for 1 H and 13 C NMR data of [R(L7 –2H) ]3− (R = Ce–Yb, except Pm, Gd) show an abrupt break near 3 the middle of the lanthanide series assigned to concomitant variations of the contact Fi and pseudo-contact B02 Gi terms (table 13, ﬁg. 34, Ouali et al. (2002)). Since eq. (51) has established the existence of a structural change (oscillation of the pyridine rings) between R = Eu and R = Tb for [R(L7 –2H)3 ]3− , the origin of the concomitant changes of Fi and B02 Gi does not require further justiﬁcations. However, the geometrical fac-

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

409

Table 13 Computed values for contact (Fi ), pseudo-contact (B02 Gi ) terms and agreement factors (AFi ) for 1 H- and 13 C-nuclei in complexes [R(L7 –2H)3 ]3− (D2 O, 298 K, pD = 6, Ouali et al. (2002)). See ﬁg. 30 for the atom-numbering scheme Compd R = Ce–Eu R = Tb–Yb

Fi B02 Gi Fi B02 Gi AFi a

H2 −0.28(1) −0.32(1) 0.03(7) −0.36(2) 0.09

H3 −0.30(3) −0.30(2) 0.02(6) −0.31(2) 0.09

C1 −0.75(4) −1.32(3) 0.3(4) −1.7(1) 0.10

C2 −3.7(2) −1.2(2) −2.6(2) −0.58(7) 0.14

C3 0.98(9) −0.80(8) 1.2(1) −0.59(3) 0.05

C4 −0.6(1) −0.1(1) −1.2(2) −0.53(6) 0.22

a AF is calculated by using δ calc obtained for R = Ce–Eu and R = Tb–Yb. i ij

para

para

Fig. 34. Plots of (a) δij /Sz j vs Cj /Sz j (eq. (48)) and (b) δij /Cj vs Sz j /Cj (eq. (49)) for C2 in [R(L7 – 2H)3 ]3− (R = Ce–Yb, D2 O, 298 K, adapted from Ouali et al. (2002)).

tor Gi can be calculated from the molecular models and changes of the crystal-ﬁeld parameter can be addressed. The use of GC3 as a reference taken from the two structural models allows the estimation of all remaining Gi factors from the experimental Rik terms obtained for the two isostructural series (table 12). B02 are computed from the pseudo-contact terms B02 Gi collected in table 13, thus leading to B02 (R = Ce–Eu) B02 (R = Tb–Yb)

= 1.5(1).

The latter ratio parallels a similar trend observed for [R(L7–2H)3 ]3− doped in single hexagonal crystals of Na3 [Yb1−x Rx (L7 –2H)3]·NaClO4 ·10H2 O, and for which B02 = −272 cm−1 (R = Eu), B02 = −140 cm−1 (R = Tb) and B02 = −198 cm−1 (R = Dy) which correspond to an average ratio B02 (R = Eu) B02 (R = Tb–Dy)

= 1.6(1)

410

C. PIGUET AND C.F.G.C. GERALDES para

para

para

para

(Hopkins et al., 1996). Finally, plots of δij /δkj vs δlj /δkj according to the three-nuclei method (eq. (53)) conﬁrm the abrupt break occurring near the middle of the series (Ouali et al., 2002). The experimental slopes (Sik − Rik ) (Slk − Rlk ) and intercepts (Slk Rik − Sik Rlk ) (Slk − Rlk ) depend on Fi and Gi parameters and they can be satisfactorily predicted from Fi terms obtained with eqs. (48), (49) and Gi terms resulting from the combination of structural modeling and eq. (51). Compared to the original report of Reilley et al. (1975) proposing the invariance of Gi , Fi and B02 along the complete lanthanide series, the recent re-examination of the new complete set of NMR data by Ouali et al. (2002) reaches opposite conclusions and eventually establishes a concomitant change of Gi , Fi and B02 between R = Eu and R = Tb. This discrepancy originates from (i) the too limited set of data collected by Reilley et al. (1975) for the light lanthanides and (ii) by fortuitous compensation effects produced by the concomitant variations of Gi and B02 for H2, H3 and C3 which indeed provide invariant pseudo-contact terms B02 Gi along the complete series for these NMR signals. A similar treatment applied to the analogous complexes [R(L3 )3 ]3+ indicates that related oscillations of the pyridine rings are responsible for the observed structural changes. Although only a rough molecular modeling has been proposed for [R(L3 )3 ]3+ , a similar behaviour is evidenced with a concomitant change of Gi , Fi and B02 between R = Tb and R = Er and an approximate ratio B02 (R = Ce–Tb) B02 (R = Er–Yb)

= 3(1)

(Ouali et al., 2002). 3.1.8. [R(L8 –3H)] (L8 = 1,4,7-triazacyclononane-N ,N ’,N ”-triacetic acid) The potentially hexadentate triaza macrocyclic ligand L8 (its trianion form is also known as NOTA3− ) forms thermodynamically quite stable [R(L8 –3H)(H2O)q ] complexes in aqueous solution, with log β1 values increasing from 13.4 for R = La to 15.9 for R = Lu (Cacheris et al., 1987). Although none of the complexes of the series has so far been isolated and characterized in the solid state by X-ray crystallography, the ligand structure makes these chelates good candidates for C3 symmetry. A study of the lanthanide(III) induced 17 O shifts of water solutions of these complexes has shown that their hydration number q changes across the lanthanide series, from q = 3–4 in the ﬁrst half (R = Ce–Eu) to q = 3 in the second half of the series (R = Dy–Yb) (Bryden et al., 1981). This is consistent with the ﬂuorescence data available for the Eu3+ complex in aqueous solution, where two different species are observed in equilibrium (Bryden et al., 1981). The 1 H and 13 C NMR spectra of the whole series of [R(L8 –3H)(H2O)q ] complexes have been also analyzed in terms of their structure and dynamics in solution (Geraldes et al., 1985;

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

411

Fig. 35. Schematic representation of L8 (NOTA) coordinated to a lanthanide ion (one of the acetate arms is not shown for clarity) with a geometry in accordance with the best ﬁt of the LIR and LIS data, illustrating the dipolar angle effect (+ and − indicate the sign of the geometric factor Gi ) (Sherry et al., 1986).

Sherry et al., 1986). In particular, the 1 H and 13 C LIS values have been reported for all the paramagnetic ions except Ce, Pm and Gd in D2 O (10−1 mol · dm−3 , pH = 6.0 and 343 K, Sherry et al. (1986)). The symmetry of the spectra obtained shows that the chelates indeed have C3 symmetry in solution, and the absolute values and signs of the LIS values are clear indication that R(III), although bound to the three N-atoms and to the carboxylate oxygens, does not ﬁt inside the macrocyclic cavity but is located well above (2.2 Å) the plane of the three nitrogens (ﬁg. 35). All ethylenediamine groups in the 9-membered macrocyclic ring adopt an identical gauche conformation, either δ or λ, leading to one of two possible square [333] conformations. The fast interconversions between the two gauche conformations of the ethylene bridges, corresponding to a high conformational ﬂexibility of the macrocycle, explain their AA XX proton spectrum at all temperatures. para para Plots of δij /Sz j vs Cj /Sz j (eq. (48)) and δij /Cj vs Sz j /Cj (eq. (49)) for 1 H and 13 C NMR data of [R(L8 –3H)(H O) ] (R = Pr–Yb, except Pm, Gd) show an abrupt break 2 q near the middle of the lanthanide series reﬂecting variations of the Fi and B02 Gi parameters (table 14, ﬁg. 36, Sherry et al. (1986)). On the basis of these results, as well as of the 17 O NMR and luminescence data, the original work assumed that B02 did not change and that two groups of solution structures were present, with a change of ligand coordination number or hydration number at Tb. The simultaneous least-squares ﬁts of lanthanide induced relaxation (LIR, T1 ) according to eq. (18) and lanthanide induced shifts (LIS) according to eq. (47) with a chemical model for the [R(L8 –3H)(H2O)q ] chelates based on the modiﬁed crystal structure of the Cr3+ complex gave different best ﬁt structures. While for the later ions (R = Dy–Yb) the ligand is hexa-coordinated with three inner-sphere water molecules (ﬁg. 35), it is concluded that the earlier chelates (R = Pr–Eu) adopt a structural mixture of hexa- and penta-coordinate (with one free acetate arm) ligands with three and four inner-sphere water molecules, respectively. The application of the two-nuclei crystal-ﬁeld independent technique and the three-nuclei method provide convincing evidence for the proposed structural subdivision of the [R(L8 – para para 3H)(H2 O)q ] complexes (Geraldes et al., 2003). All the plots of δij /Sz j vs δkj /Sz j

412

C. PIGUET AND C.F.G.C. GERALDES

Table 14 Computed values for contact (Fi ), pseudo-contact (B02 Gi ) terms and R 2 values, according to eq. (48), comparison of Rik and (Fi −Rik Fk ) parameters calculated directly according to eq. (51), and α and β parameters calculated directly according to eq. (53), with those obtained from the above Fi and B02 Gi terms, for 1 H- and 13 C-nuclei in complexes [R(L8 –3H)(H2 O)q ] (R = Pr–Yb, D2 O, pD = 6.0, 343 K, Sherry et al. (1986)). See ﬁg. 35 for the atom-numbering scheme Compd R = Pr–Tba

Fi B02 Gi R2

Compd R = Dy–Ybb

Compd R = Pr–Tba

Compd R = Dy–Ybb

Compd R = Pr–Tba

Compd R = Dy–Ybb

Ha 0.37 −0.12

Fi B02 Gi

0.914 Ha 0.75 0.04

R2

0.799

Rik (exp) (Fi −Fk Rik )(exp) R2 Rik (calc) (Fi −Fk Rik )(calc) Rik (exp) (Fi −Fk Rik )(exp) R2 Rik (calc) (Fi −Fk Rik )(calc) α(exp) β(exp) R2 α(calc) β(calc) α(exp) β(exp) R2 α(calc) β(calc)

HN’ 0.36 −0.23

HN” 0.38 −1.18

CO −3.19 3.37

Ca −2.37 0.30

CN −4.15 −2.32

0.704 HN’ 0.15 −0.08

0.552 HN” 0.97 −0.43

0.999 CO −4.15 2.06

0.881 Ca −3.00 0.33

0.985 CN −0.58 −0.27

0.730 0.905 CN –CO Ca –CO Ca –CN −0.69 0.11 −0.16 −6.35 −2.18 −3.18 0.976 0.917 0.958 −0.69 0.09 −0.13 −6.32 −2.09 −2.91 CN –CO Ca –CO Ca –CN −0.17 0.18 −1.05 −0.90 −2.42 −3.36 0.901 0.937 0.958 −0.13 0.16 −1.22 −1.12 −2.34 −3.71 i = CN ; k = Ca ; l = CO −0.97 2.96 0.981 −1.38 2.99 i = CN ; k = Ca ; l = CO −0.24 0.31 0.960 −0.21 0.40

0.914 HN’ –Ha 1.02 −0.13 0.956 1.92 −0.35 HN’ –Ha −0.22 0.36 0.908 −2.00 1.65

0.704 0.552 HN’ –HN” HN” –Ha 0.15 7.35 0.25 −2.62 0.991 0.970 0.20 9.83 0.28 −3.26 HN’ –HN” HN” –Ha 0.05 −3.71 −0.11 3.87 0.953 0.962 0.19 −10.75 −0.14 8.99 i = HN” ; k = Ha ; l = HN” 16.76 −10.43 0.895 9.33 8.72 i = HN” ; k = Ha ; l = HN” 16.05 −1.58 0.961 5.65 −6.39

a Values for the ﬁrst isostructural series (except Ce and Sm). b Values for the second isostructural series.

(eq. (51)), which eliminate the effect of any changes of B02 , either involving the three types of carbon nuclei or the three types of protons, systematically display two different straight lines for R = Pr–Tb and R = Dy–Yb (ﬁg. 37a), conﬁrming that the Fi and Gi parameters change abruptly at Tb. There is generally a good agreement of experimental and calculated Rik and

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

413

(a)

(b)

para

Fig. 36. Plots of (a) δij /Sz j para vs Cj /Sz j and (b) δij /Cj vs Sz j /Cj for CN in [R(L8 –3H) (H2 O)q ] (R = Pr–Tb, Dy–Yb, D2 O, 343 K, redrawn from Sherry et al. (1986)).

(Fi −Fk Rik ) parameters (table 14). Since in the present system Gi values change, B02 ratios, B02 (R = Ce–Tb) B02 (R = Dy–Yb)

, para

para

para

para

could not be obtained. Plots of δij /δkj vs δlj /δkj (eq. (53)) (see ﬁg. 37b) conﬁrm the abrupt break near the middle of the series. The experimental slope α=

(Sik − Rik ) (Slk − Rlk )

414

C. PIGUET AND C.F.G.C. GERALDES

(a)

(b)

Fig. 37. (a) Crystal-ﬁeld independent para para plot of δij /Sz j vs δkj /Sz j for the para

para

CN –CO pair; (b) plot of δij /δkj vs para para δlj /δkj according to the three-nuclei method for the triad CN , CO and Ca in [R(L8 –3H)(H2 O)q ], R = Ce–Yb, D2 O, 298 K (redrawn from Geraldes et al. (2003)).

and intercept β=

(Slk Rik − Sik Rlk ) (Slk − Rlk )

parameters are in satisfactory agreement with those calculated from predicted from Fi and Gi terms obtained form the other methods (table 14). The results described here ﬁrmly support the literature conclusion of a structural change between the light and heavy [R(L8 –3H)(H2O)q ] complexes. In this case, the breaks in the plots likely reﬂect a change in the geometric terms, Gi and Fi , as they are independent of any concomitant changes of the crystal ﬁeld parameter.

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

415

3.2. Complexes with fourfold symmetry 3.2.1. [R(L9 –H)4 ]− (L9 = dithiomethylphosphinic acid and dithiophosphorus acid and dithiophosphorus acid derivatives) A large number of lanthanide complexes of the type [R(L9 –H)4 ]− have been isolated and characterized in the solid state by X-ray crystallography, where the ligand [L9 –H]− , with two sulphur donor atoms and general formula R2 PS− 2 , is a dithiophosphinate (e.g., R = Me) or a dithiophosphonate (R = OMe, OEt, OPri ) (Pinkerton and Schwarzenbach, 1981; Spiliadis et al., 1982, 1983). The crystal structures show that the lanthanide is coordinated to eight sulphur atoms with coordination geometries ranging between the regular D2d dodecahedron, favored by alkoxy substituents at phosphorus, and a dodecahedron distorted towards the D2 square antiprism, favored by alkyl substituents. However for each ligand no structural change was observed along the lanthanide series in the solid state. 31 P and 1 H LIS data have been reported for these [R(S PR ) ]− complexes in CD Cl so2 2 4 2 2 lution (R = Ce–Yb, except Pm and Gd). Measurements were carried out at 299 K for all complexes (R = OEt (S2 P(OEt)− 2 = O,O’-diethyl dithiophosphate) (Pinkerton and Earl, 1978); R = CH3 , Spiliadis and Pinkerton (1982); R = OMe, OPri , Spiliadis and Pinkerton (1983)) and also at 233 K for R = OEt (Pinkerton and Earl, 1978). The observed NMR data ﬁt an effectively axial symmetric coordination model in which the lanthanide ion is chelated by four S2 PR2 2− molecules in a bidentate fashion (through the two sulfur atoms). These data were para para analysed using a simpliﬁed version of eq. (51) by plotting δij /Sz j vs δkj /Sz j , where i is the 31 P nucleus and k are the CH2 and CH3 protons and assuming no contact contribution to the LIS values of these protons. In this case Fk = 0 and eq. (51) reduces to eq. (60) and the plots gave directly as intercepts the values of the hyperﬁne coupling constant to the 31 P P nucleus, FP , and as slopes the geometric ratios RPk = G Gk . para

δPj

Sz j

para

= FP +

GP δkj · . Gk Sz j

(60)

Breaks were observed in such plots for all the compounds studied, between Tb and Dy for the R = Me compound, and between Dy and Ho for the alkoxy derivatives. These breaks were assigned to structural (RPk values) and 31 P coupling constant (FP ) changes along the lanthanide series, although no difference in the solid state structures of the complexes along the series has been detected (Pinkerton and Earl, 1978; Spiliadis and Pinkerton, 1982, 1983). Large decreases of coupling constants were observed, e.g., from 1.52 MHz to 0.86 MHz for the R = OEt derivative, while for R = Me the values were smaller but still decreasing along the series (1.09 MHz to 0.51 MHz). The RPk values also decreased very much along the lanthanide series due to a substantial decrease of the dipolar shift of the 31 P nucleus, consistent with a change in solution of the coordination polyhedron from a dodecahedral to a square antiprismatic structure. para para Plots of δij /Sz j vs Cj /Sz j (eq. (48)) and δij /Cj vs Sz j /Cj (eq. (49)) for the LIS data of the [R(S2 P(OEt)2 )4 ]− complexes at 299 K and 233 K show breaks at Tb, reﬂecting variations of the Fi and B02 Gi terms (table 15, ﬁg. 38, Geraldes et al. (2003)). It can be seen

416

C. PIGUET AND C.F.G.C. GERALDES

Table 15 Computed values for contact (Fi ), pseudo-contact (B02 Gi ) terms and R 2 values, according to eq. (48), comparison of Rik and (Fi −Rik Fk ) parameters calculated directly according to eq. (51), and α and β parameters calculated directly according to eq. (53), with those obtained from the above Fi and B02 Gi terms, for 1 H- and 31 P-nuclei in complexes [R(L9 –H)4 ]− (R = Ce–Yb, [L9 –H]− = S2 P(OEt)− 2 , CD2 Cl2 , Pinkerton and Earl (1978)) Compd R = Ce–Eua

CH2 Fi B02 Gi

0.35 0.37

0.12 0.13

R2

0.928 CH2

0.920 CH3

Compd R = Tb–Ybb

Fi B02 Gi R2

−0.35 0.56 0.988

Compd R = Ce–Eua

R = Tb–Ybb

T = 253 K CH3

Rik (exp) (Fi −Fk Rik )(exp) R2 Rik (calc) (Fi −Fk Rik )(calc) Rik (exp) (Fi −Fk Rik )(exp) R2 Rik (calc) (Fi −Fk Rik )(calc)

Compd

CH2

56.43 22.65

0.18 0.21

0.07 0.07

0.950 CH2

0.931 CH3

0.923 P

−0.13 0.20

−0.23 0.28

49.90 −0.10

0.986 CH3 –CH2

T = 296 K CH3

P

0.994 P–CH3

0.36 −0.01 0.999 0.34 0.00 0.37 −0.01 0.998 0.35 0.00 i = CH3 ; k = P; l = CH2

c c c c c c c c c c

0.967

P 49.38 14.83

−0.09 0.10

0.962 P 38.90 −0.48

0.947 CH3 –CH2 0.37 −0.01 0.998 0.35 0.00

0.994 P–CH3 86.03 56.31 0.826 200.4 36.16

0.37 −3.31 −0.01 39.81 0.998 0.276 0.37 −1.07 −0.01 38.74 i = CH3 ; k = P; l = CH2

R = Ce–Eua

α(exp) β(exp) R2 α(calc) β(calc)

0.36 0.00 0.999 0.34 0.09

0.36 0.00 0.999 0.35 0.00

R = Tb–Ybb

α(exp) β(exp) R2 α(calc) β(calc)

0.36 0.00 0.999 0.37 0.00

0.36 0.00 0.999 0.37 0.00

a Values for the ﬁrst isostructural series (except Sm). b Values for the second isostructural series. c Not determined.

that proton Fk values are very small and FP values, as well as RPk values indeed decrease drastically at Tb, in particular, the large FP couplings by about 50% in the second part of the R series. para para The plots of δij /Sz j vs δkj /Sz j (eq. (51)) for i = CH3 and k = CH2 give a single straight line identical at both temperatures indicating that the structural change is not reﬂected

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

417

para

Fig. 38. Plot of δij /Sz j vs Cj /Sz j for CH3 and CH2 protons in [R(L9 –H)4 ]− , [L9 –H]− = S2 P(OEt)− 2 (R = Ce–Yb, CD2 Cl2 , 253 K, adapted from Pinkerton and Earl (1978), Geraldes et al. (2003)).

in the proton Gi and Fi parameters, e.g., GCH3 /GCH2 is constant (ﬁg. 39a). However, plots with i = P and k = CH2 or CH3 , identical to those discussed above using eq. (60) (ﬁg. 39b), gave breaks at Tb, conﬁrming that the Fi and Gi parameters change abruptly at Tb. There is generally a good agreement of experimental and calculated Rik and (Fi −Fk Rik ) parameters (table 15). In the ﬁtting of the early R plots, Eu and Sm are excluded due to the contribution of excited states to the Sz and Cj parameters. Since in the present system Gi values change, the B02 ratios B02 (R = Ce–Tb) B02 (R = Dy–Yb) could not be obtained. para para para para Plots of δij /δkj vs δlj /δkj (eq. (53)) with i = CH3 , l = CH2 and k = P give a single straight line along the lanthanide series (ﬁg. 39c), with experimental slopes and intercepts identical at both temperatures (α = 0.366; β = 0) (table 15). This is not surprising given that the temperature-dependent parameters, B02 , Sz j and Cj , are all absent from eq. (53). The experimental α=

(SCH3 P − RCH3 P ) (SCH2 P − RCH2 P )

β=

(SCH2 P RCH3 P − SCH3 P RCH2 P ) (SCH2 P − RCH2 P )

and

parameters are in satisfactory agreement with those calculated from Fi and Gi values obtained by the other methods (table 15). However, plots according to eq. (53) with other combinations, such as for i = P, l = CH3 and k = CH2 , give breaks, and thus conﬁrm the structural and coupling constants change. The reason why the ﬁrst plot is not sensitive to the structural

418

C. PIGUET AND C.F.G.C. GERALDES

(a)

(b)

para

para

Fig. 39. Crystal-ﬁeld independent plot of δij /Sz j vs δkj /Sz j (a) for the CH3 –CH2 pair; (b) for the P–CH2 para para para para pair; (c) Plot of δij /δkj vs δlj /δkj for the CH3 , CH2 , P triad at 253 K (P) and 296 K (F). Data for [R(L9 –

H)4 ]− , [L9 –H]− = S2 P(OEt)− 2 (R = Ce–Yb, CD2 Cl2 , 296 K, adapted from Pinkerton and Earl (1978), Geraldes et al. (2003)).

change is that β = 0 which implies that GCH2 FCH2 = FCH3 GCH3 and these ratios do not change along the series. This example illustrates that both the two nuclei and three nuclei methods may accidentally not reﬂect structural and/or Fi changes for

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

419

(c)

Fig. 39. Continued.

some of the combinations of nuclei used in the plots. Thus, it is important to analyse all the possible combinations. 3.2.2. [R(L10 –4H)]− (L10 = 1,4,7,10-tetraazacyclododecane-N ,N ’,N ”,N ”’-tetraacetic acid) The eight donor atoms of the macrocyclic ligand L10 (usually know as DOTA) may produce square antiprismatic eight-coordinated structures, with the four ring nitrogens deﬁning one of the square faces in the coordination polyhedron and the four coordinated pendant arm oxygens deﬁning the other one (ﬁg. 40). The twist angle α between the planes formed by the four oxygens and the four nitrogens can be positive or negative, leading to two possible isomers, the square antiprismatic (SAP) (designated M’) and the inverted SAP (m’). In these two isomers, the macrocyclic rings have the same conformation and the difference between them is in the layout of the pendant arms. In these structures two structurally independent elements of chirality are present deﬁned by the pendant arm C4 –C3 –N–C1 and ring N–C1 –C2 –N torsion angles (ﬁg. 41). The 12-membered macrocyclic ring may adopt two enantiomeric square [3333] conformations, given as δδδδ and λλλλ (with respect to each ﬁve-membered ring chelate), and the pendant arms may be arranged in either a clockwise () or counterclockwise () manner, leading to four possible stereoisomers. These constitute two diastereoisomers each with enantiomeric pairs which are not distinguishable by NMR spectroscopy in solution: M’ with enantiomers (δδδδ) and (λλλλ), and m’ with enantiomers (δδδδ) and (λλλλ) (ﬁg. 42). X-ray crystal structures have been determined for a series of [R(L10 –4H)]− chelates, deﬁning nine-coordinate capped square antiprismatic (CSAP) or inverted capped square antiprismatic structures. The acetate arms of the L10 or DOTA ligand are arranged in a propeller-like fashion above the basal plane made up of the four N donor atoms, which encompass the

420

C. PIGUET AND C.F.G.C. GERALDES

Fig. 40. Schematic representation of the M and m isomers, as well as of the M’ and m’ isomers, for tetraazamacrocyclic complexes of R(III) (adapted from Geraldes et al. (2003)).

Fig. 41. Model of a part of the structure of complexes [R(L10 –4H)]− in the (λλλλ) enantiomeric form of the M isomer. Symmetry-related atoms are not shown for clarity. The numbering scheme for hydrogen and carbon/phosphorous atoms is also shown. H5 denotes the pro-R and H6 the pro-S pendant arm methylene proton (adapted from Ren et al. (2002)).

R(III) ion, deﬁning another plane above it, and thereby generating a C4 symmetry axis in these complexes. The X-ray structures of the [R(L10 –4H)]− complexes with R = Eu, Gd, Y and Lu are CSAP, with twist angles α of ca 39◦ (Spirlet et al., 1984; Dubost et al., 1991; Chang et al., 1993; Parker et al., 1994; Aime et al., 1996; Benetollo et al., 1999), whereas the La complex adopts an inverted CSAP structure in which α = −22◦ (Aime et al., 1997a). The

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

421

Fig. 42. Schematic representation of the structures and dynamics of [R(L10 –4H)]− complexes, looking down along the R-water O bond. The water molecule is omitted for clarity (adapted from Frullano et al. (2002)).

numbering scheme for the hydrogen and carbon atoms is shown in ﬁg. 41, which schematically represents part of the structure of the complexes in the (λλλλ) enantiomeric form of the M isomer, where H5 denotes the pro-R and H6 the pro-S pendant arm methylene protons. This notation is in agreement with solution NMR work for the L10 (DOTA) complexes (Aime et al., 1992b; Marques et al., 1995). The 1 H and 13 C NMR spectra of the [R(L10–4H)]− (R = La–Lu, except Pm and Gd) complexes in D2 O at pH = 7 at different temperatures have been published and the LIS values for both 1 H and 13 C nuclei were reported (Desreux, 1980; Aime et al., 1992a, 1992b, 1997b; Hoeft and Roth, 1993; Marques et al., 1995). The 1 H and 13 C NMR spectra exhibit two sets of resonances corresponding to the presence of two slowly interconverting coordination isomers, one set of resonances having constantly larger frequency shifts than the other group. The isomer displaying larger shifts corresponds to a nine-coordinate CSAP structure M, while the isomer displaying smaller shifts is either a nine-coordinate inverted CSAP m (from La to Ho), or an eight-coordinate inverted SAP m’ structure (Er to Lu) (Aime et al., 1992a, 1992b, 1997b). In addition to the frequency difference, the two isomers also differ in population. The relative intensities observed for the two sets of NMR resonances showed that while the m isomer dominates for the larger cations, La–Nd, the M isomer becomes the most stable for the smaller cations Sm–Ho, with a gradual increase of the M/m ratio from

422

C. PIGUET AND C.F.G.C. GERALDES

Fig. 43. Conformational and coordination equilibria for the [R(L10 –4H)]− complexes in aqueous solution (adapted from Aime et al. (1997a)).

La to Ho. In all these cases, the isomerization process is purely conformational, as shown by the near zero reaction volumes obtained by high-pressure NMR (Aime et al., 1997b). Then, a steady decrease of the M population occurs from Er to Lu. The large positive isomerization volumes obtained show that the minor isomer results now from a fast water dissociation process superimposed on the conformational rearrangement leading to an eight-coordinate square antiprismatic (SAP) geometry, m’ and a decrease of the M/m’ ratio (ﬁg. 43) (Aime et al., 1997b). Besides the size of the R(III) ion, the relative concentrations of the two species, also depend on temperature, pressure and on the concentration of added inorganic salts. High concentrations of non-coordinating salts stabilize the m form relative to M. The solution structure of the CSAP isomer M is consistent with the X-ray crystal structures of the Eu, Gd, Y, Ho and Lu complexes of L10 , while the structure of the inverted CSAP isomer is consistent with the X-ray structures of its La complex. This similarity between the solid state and the solution structures of the isomers was initially shown by the excellent agreement between the Yb induced 1 H shifts (of the M isomer), which are assumed to be almost purely of pseudocontact origin (eq. (29)), and shifts calculated from the X-ray structure of the Eu complex, applying the axial model, since that structure has a C4 symmetry axis (Desreux, 1980). Later, this approach was extended to the shifts of the m’ isomer of the Yb complex, supported by the comparison of the experimental distances between the R(III) ion and the ligand protons in the M and m’ isomers of the Tb–Yb complexes, evaluated through the Curie relaxation contribution (eqs. (15)–(17)), and calculated from structural models (Aime et al., 1992a, 1992b). It was concluded that the structure of the macrocyclic rings is the same in both isomers, and that the difference between the two is in the layout of the acetate arms. This difference in the arrangement of the acetates leads to a twisted capped square antiprismatic structure (twisted or inverted CSAP) which contains a layout of the acetate arms that is inverted with respect to that in the main isomer, corresponding to a negative and smaller twist angle between the N4 and O4 planes. The use of variable temperature 13 C NMR on the Nd3+ -complex and 1 H EXSY on the Yb-complex (Aime et al., 1992b), and for the Eu and Yb complexes (Hoeft and Roth, 1993), demonstrated the exchange processes occurring between the isomers in solution. The dynamics of this system is summarized in ﬁg. 42. The four stereoisomers (two pairs of enantiomers) can interconvert in solution by either ring inversion ((δδδδ) ⇔ (λλλλ)) or ac-

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

423

etate arm rotation ( ⇔ ). Either process alone results in exchange between the CSAP and twisted CSAP geometries and both processes combined, either in succession or concerted, result in an exchange between enantiomeric pairs (see ﬁg. 42). A thorough quantitative analysis of variable temperature 1 H EXSY and variable temperature 13 C NMR studies were performed on [Yb(L10)]− by completely solving the dynamic matrix (Jacques and Desreux, 1994). It was shown that each species in the dynamic equilibrium is exchanging with all other species and that, for this system, arm rotation is faster than ring inversion, reﬂecting the high rigidity of the R(III) complexes of DOTA. The 1 H and 13 C LIS data available for the M and m isomers of the [R(L10 –4H)]− compara para plexes were analyzed by plots of δij /Sz j vs Cj /Sz j (eq. (48)) and δij /Cj vs Sz j /Cj (eq. (49)) (Ren et al., 2002). Because Sm, as usual, was excluded from these plots, and, due to population limitations, 1 H and 13 C LIS values of the M isomer were only available for R = Nd–Eu in the ﬁrst half of the lanthanide series, and 13 C LIS values for m in the second half of the series were only available for Yb (m’), in these cases not enough R(III) data were available for a deﬁnite conclusion. However, with the available data, breaks between light and heavy lanthanide ions were observed in most of these plots (see ﬁg. 44 for some examples), as reported before (Marques et al., 1995), reﬂecting variations of the contact Fi and pseudocontact B02 Gi parameters. Systematic deviations were also observed for Tm and Yb from the linear correlations deﬁned by the other R(III) ions within the second half of the series. The linear correlation coefﬁcient R 2 and the values of Fi and B02 Gi were evaluated for each proton and 13 C nucleus using those equations by subdivision of the lanthanides into two subgroups (Ce–Eu and Tb–Yb) and without such a subdivision (Ce–Yb) (table 16). All the protons and 13 C nuclei of the m isomer show poor linear correlations for the (Ce–Yb) data (R 2 < 0.83), which, due to the breaks, improve signiﬁcantly when the data is divided in two groups, although the deviations at Tm and Yb give relatively low R 2 values except for H1, H5 and H6 of the m isomer, where the improvement is much better (R 2 ∼ 0.94–0.97 for (Tb–Yb)). The M isomer shows less signiﬁcant breaks, as 0.98 > R 2 > 0.92 for (Ce–Yb) does not improve much in the (Tb–Yb) data. para The same sets of LIS data were also plotted according to eq. (51), as δij /Sz j vs para δkj /Sz j , which eliminate the effect of any changes of B02 (ﬁg. 45). These plots again often do not follow a single linear correlation, but show breaks between light and heavy lanthanide ions, although much less signiﬁcant than for the previous plots. The Rik and (Fi −Rik Fk ) parameters were evaluated using that equation by subdivision of the lanthanides into two subgroups (Ce–Eu and Tb–Yb) and without such a subdivision. Their values (and R 2 values) are shown in table 17. Without subdivision, the (Ce–Yb) data gave poor R 2 values for H2, H3, C2 and C4, good R 2 values for H4 and C3, and very good R 2 values (> 0.99) for H5 and H6. For all the complexes studied, R 2 values for all nuclei improved upon separation of the data in two groups (e.g., (Tb–Yb) data gave R 2 > 0.985 in all cases), but the breaks are only statistically signiﬁcant for H4, H3, H2, C4 and C2. The Rik and (Fi −Rik Fk ) parameters evaluated directly with eq. (51) (table 17) and indirectly using the Fi and B02 Gi values from eq. (48) (table 16) were compared. The agreement is extremely good for all the Rik ratios and only reasonably good for (Fi −Rik Fk ),due to larger errors in the calculated Fi values.

424

C. PIGUET AND C.F.G.C. GERALDES

(a)

(b)

para

Fig. 44. Plots of δij /Sz j vs Cj /Sz j for H4 (F) and H6 (Q) of (a) M isomer (R = Nd–Yb); (b) m/m’ isomer (R = Ce–Yb) of [R(L10 –4H)]− (D2 O, pH = 7, adapted from Geraldes et al. (2003)).

The breaks observed in these plots indicate that the Fi and Rik parameters change at the middle of the series, together with changes of B02 . The breaks of the plots according to eq. (51) are smaller relative to the plots according to eq. (48) because of the absence of B02 in the later plots, as well as the presence of geometric ratios Rik , which may be signiﬁcantly less affected by smaller structural effects on Gi values due to the lanthanide contraction (Ren et al., 2002). para para para para Various plots of δij /δkj vs δlj /δkj (eq. (53)) were made for the 13 C shifts of the M isomer. With i = C3 or C4, l = C1 and k = C2, single straight lines are obtained along the R (R = Pr, Nd, Sm Eu, Tb, Dy, Ho, Er, Yb) series. For example, for i = C4, a good linear correlation with R 2 = 0.999 is obtained (ﬁg. 45b) with α = −2.408 and β = 2.799 values (table 18). Other plots of this type give a single line along the R series, such as for i = C2, l = C1 and k = C3, but other combinations give more or less pronounced breaks, such as for

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

425

Table 16 Computed values for contact (Fi ), pseudo-contact (B02 Gi ) terms and R 2 values, according to eq. (48), for 1 H- and 13 C-nuclei in complexes [R(L10 –4H)]− , for the M isomer (R = Nd–Yb) and m/m’ isomer (R = Ce–Yb) (D O, 2 pH = 7, Ren et al. (2002)). See ﬁg. 41 for the atom-numbering scheme Compd M isomer R = Nd–Eua

Fi B02 Gi R2

Compd M isomer R = Tb–Ybb

Fi B02 Gi R2

Compd m isomer R = Ce–Eua

Fi B02 Gi R2

Compd m isomer R = Tb–Ybb

Fi B02 Gi R2

Compd M isomer R = Nd–Eua

Fi B02 Gi R2

Compd M isomer R = Tb–Ybb

H2 −0.49 0.40

H3 −1.41 1.48

H4 0.95 5.27

H5 −0.78 −3.05

H6 −2.15 1.37

1.000 H1 −2.14 −2.64

1.000 H2 −0.63 1.01

1.000 H3 −0.25 1.20

1.000 H4 3.77 6.88

1.000 H5 −3.37 −4.75

1.000 H6 −2.53 −2.13

0.934 H1 −0.52 −0.68

0.983 H2 −0.59 −0.12

0.984 H3 −1.09 0.39

0.969 H4 0.53 2.19

0.943 H5 −0.41 −0.51

0.938 H6 −1.18 −0.98

0.947 H1 −2.04 −1.77

0.115 H2 −0.47 0.64

0.832 H3 −0.08 0.76

0.989 H4 4.50 4.45

0.968 H5 −1.95 −1.50

0.923 H6 −2.75 −3.10

0.548

0.871 C2 2.54 1.59

0.919

0.971

C3 5.51 −8.39

0.943 C4 3.56 −2.94

0.963 C1 −0.10 8.51 1.000 C1 3.63 4.09

1.000 C2 3.27 1.11

1.000 C3 2.53 −4.68

1.000 C4 −1.54 −6.70

Fi B02 Gi

0.979 C1 4.64 4.93

0.959 C2 3.33 2.59

0.940 C3 1.87 0.23

0.985 C4 2.41 0.42

R2

0.985

0.984

0.050

0.166

Fi B02 Gi R2

Compd m isomer R = Ce–Eu

H1 −0.48 −1.48

a Values for the ﬁrst isostructural series (except Sm). b Values for the second isostructural series.

i = C4, l = C1 and k = C3, and for i = C2 or C3, l = C1 and k = C4 (see table 17 for the experimental α and β values, Geraldes et al. (2003)). This is in agreement with the detected changes of Fi and Gi parameters at the middle of the R series and again illustrates the fact that in this case still some of the plots according to eq. (53) may be accidentally linear. In the case of the 13 C shifts of the m isomer, the data available only for Pr, Nd and Eu gives linear plots within the ﬁrst half of the R series (see table 18). para para para para Plots of δij /δkj vs δlj /δkj (eq. (53)) obtained for the 1 H LIS data of the M and m isomers, e.g., for i = H3, H5 and H6, l = H1 and k = H4 support these conclusions (see ﬁg. 45c for the m isomer). All these plots show two linear parts with breaks in the middle of the series and table 18 compares the α and β values calculated for the two isomers.

426

C. PIGUET AND C.F.G.C. GERALDES

Table 17 Comparison of Rik and (Fi −Rik Fk ) parameters calculated directly according to eq. (51), with those obtained from the Fi and B02 Gi values obtained from eq. (48) (table 16) for the 1 H- and 13 C-nuclei in complexes [R(L10 –4H)]− , for the M isomer (R = Nd–Yb) and m/m’ isomer (R = Ce–Yb) (D2 O, pH = 7, Ren et al. (2002)). See ﬁg. 41 for the atom-numbering scheme Compd M isomer R = Pr–Eua

Compd M isomer R = Tb–Ybb

Compd m isomer R = Ce–Eua

Compd m isomer R = Tb–Ybb

Rik (exp) (Fi −Fk Rik )(exp) R2 Rik (calc) (Fi −Fk Rik )(calc) Rik (exp) (Fi −Fk Rik )(exp) R2 Rik (calc) (Fi −Fk Rik )(calc) Rik (exp) (Fi −Fk Rik )(exp) R2 Rik (calc) (Fi −Fk Rik )(calc) Rik (exp) (Fi −Fk Rik )(exp) R2 Rik (calc) (Fi −Fk Rik )(calc)

H2–H1 −0.27 −0.62 0.960 −0.27 −0.62 H2–H1 −0.37 −1.34 0.963 −0.38 −1.44 H2–H1 −0.42 −1.29 0.871 0.18 −0.50 H2–H1 −0.37 −12.4 0.979 −0.36 −1.20

H3–H1 −1.00 −1.89 0.973 −1.00 −1.62 H3–H1 −0.44 −1.10 0.972 −0.45 −1.21 H3–H1 −0.59 −1.43 0.941 −0.57 −1.39 H3–H1 −0.44 −1.02 0.966 −0.43 −0.96

H4–H1 −3.56 −0.78 0.989 −3.56 −0.75 H4–H1 −2.56 −1.42 0.990 −2.61 −1.82 H4–H1 −3.12 −0.90 0.980 −3.22 −1.14 H4–H1 −2.57 −0.85 0.990 −2.51 −0.62

H5–H1 2.06 0.22 0.999 2.06 0.21 H5–H1 1.79 0.42 0.999 1.80 0.48 H5–H1 0.73 −0.05 0.988 0.75 −0.02 H5–H1 0.85 −0.23 0.999 0.85 −0.22

H6–H1 −0.93 −2.60 0.997 −0.93 −2.60 H6–H1 0.81 −0.84 0.999 0.81 −0.80 H6–H1 1.46 −0.39 0.998 1.44 −0.43 H6–H1 1.77 −0.90 0.997 1.75 −0.82

C2–C1 0.19 2.56 1.000 0.19 2.56 C2–C1 0.26 2.36 0.924 0.27 2.29 C2–C1 0.53 0.89 1.000 0.53 0.87 C2–C1

C3–C1 −0.99 5.42 1.000 −0.99 5.42 C3–C1 −1.15 6.77 0.977 −1.14 6.67 C3–C1 0.07 1.36 0.118 0.05 1.63 C3–C1

C4–C1 −0.35 3.52 1.000 −0.35 3.53 C4–C1 −1.63 4.33 0.998 −1.64 5.05 C4–C1 0.11 1.72 0.267 0.09 1.99 C4–C1

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

a Values for the ﬁrst isostructural series (except Sm). b Values for the second isostructural series. c Not determined.

3.2.3. [R(L11 )]3+ (L11 = 1,4,7,10-tetraazacyclododecane -1,4,7,10-tetrakis(N ,N -diethylacetamide)) Although no crystal structure is available for any of the [R(L11)]3+ complexes, where L11 is the DOTA-like tertiary tetraamide derivative DOTEA, the known crystal structures of R(III) complexes for various DOTA-like achiral primary and secondary tetramide derivatives (ﬁg. 46) are available. These structures are variable, with m structures for [La(DOTAM)(H2O)]3+ (Morrow et al., 1993) and [Eu(DOTAM)(H2O)]3+ (Amin et al., 1994) (twist angles between the planes of the O4 and N4 atoms of −26.5◦ and −30 ◦ , respectively), and M structures for [R(DTMA)(H2O)]3+ (R = Gd, Dy, twist angles of ca 40◦ ) (Bianchi et al., 2000; Aime et al., 1999b). However, in solution it was found that the m/M isomer ratio increased from 0.19 for [Eu(DOTA)]−, to 0.25 for the primary tetraamide derivative [Eu(DOTAM)]3+, to 0.31 for the secondary tetraamide [Eu(DTMA)]3+, and to 2 for the tertiary tetraamide [Eu(DOTTA)]3+, indicating that increasing steric demand at the bound metal ion favors the inverted square antiprismatic structure m (Aime et al., 1999b).

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

427

(a)

(b)

para

para

Fig. 45. (a) Crystal-ﬁeld independent plots of δij /Sz j vs δkj /Sz j for the H5–H1 (F) and H6–H1 (2) pairs para para para para of the M isomer; Plots of δij /δkj vs δlj /δkj ; (b) for the C4, C1, C2 triad of the M isomer; (c) for the Hi, H1, H4 triads (Hi = H3 (F), H5 (Q), H6 (")) of the m isomer ([R(L10 –4H)]− , D2 O, pH = 7, adapted from Geraldes et al. (2003)).

The 1 H and 13 C LIS values of the [R(L11 )]3+ (R = Ce–Yb except Pm and Gd) complexes, were obtained in CD3 CN at 253 K (the 13 C LIS data are available only for Pr, Nd, Sm and Eu complexes) (Forsberg et al., 1995), where only one set of NMR signals was found in solution. para The 1 H LIS data were ﬁrst analysed using plots of δij /Sz j vs Cj /Sz j (eq. (48)) and para δij /Cj vs Sz j /Cj (eq. (49)). The shift data for the Tm complex signiﬁcantly deviated from those of other complexes, and the plots showed breaks near the middle of the lanthanide series, reﬂecting variations of the Fi and B02 Gi parameters. The geometric factor values derived from the two subgroups differed by as much as 30% for the six protons located three bonds

428

C. PIGUET AND C.F.G.C. GERALDES

(c)

Fig. 45. Continued.

Fig. 46. Chemical structure of various DOTA-like tetramide derivative ligands.

away from the lanthanide ions (H1–H6) and the corresponding differences in the hyperﬁne coupling constant were as much as 600% (Forsberg et al., 1995). The 1 H LIS data were also analysed taking the magnetic anisotropy constant D1 = (χzz − (1/3) Tr χ) = Cj B02 as a variable and comparing the data with the geometric factor values obtained from a structure of these complexes derived by a MM2 calculation using speciﬁed geometric restrictions. This calculated structure was of the CSAP (M) type, with a twist angle of 47◦ between the planes of the O4 and N4 atoms. The results further suggested a signiﬁcant difference in Gi values between the light and heavy [R(L11 )]3+ complexes. The derived (χzz − (1/3) Tr χ) values for the series of [R(L11 )]3+ complexes did not follow the trend of Bleaney’s Cj constants, which was interpreted as due to a change of the crystal ﬁeld parameter B02 along the lanthanide series, with the largest value for Tm.

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

429

Table 18 Comparison of α and β parameters calculated directly according to eq. (53), with those obtained from the Fi and B02 Gi values obtained from eq. (48) (table 16) for the 1 H- and 13 C-nuclei in complexes [R(L10 –4H)]− , for the M isomer (R = Nd–Yb) and m/m’ isomer (Ce–Yb) (D2 O, pH = 7, Ren et al. (2002), Geraldes et al. (2003)). See ﬁg. 41 for the atom-numbering scheme Compd M isomer R = Pr–Eua Compd M isomer R = Tb–Ybb

Compd m isomer R = Ce–Eua

Compd m isomer R = Tb–Ybb

i = H2 α(exp) β(exp) R2

k = H4; l = H1 i = H3 i = H5

c

c

c

c

c

c

c

c

c

α(exp) β(exp) R2

i = H2 3.11 1.28 0.975

α(exp) β(exp) R2

i = H2 1.48 0.44 0.67

α(exp) β(exp) R2

i = H2 1.74 0.86 0.60

i = H3 i = H5 2.17 0.80 0.97 −0.37 0.976 0.976 k = H4; l = H1 i = H3 i = H5 1.88 2.20 0.74 0.22 0.93 1.00 k = H4; l = H1 i = H3 i = H5 1.54 −0.01 0.80 −0.72 0.69 0.11

k = C2; l = C1 i = C3 i = C4 c −2.04 −2.41 c 2.50 2.80 c 0.999 1.00 i = H6 i = C3 i = C4 3.00 −2.04 −2.41 0.80 2.50 2.80 0.97 0.999 1.00 i = H6

i = H6 0.40 −0.12 0.98 i = H6 1.25 0.17 0.96

k = C3; l = C1 k = C4; l = C1 i = C2 i = C2 i = C3 c c 0.67 c c 0.42 c c 0.98 i = C2 i = C2 i = C3 0.67 1.43 0.64 0.42 0.59 1.13 0.98 0.712 0.50 k = C3; l = C1 i = C2 i = C4 0.73 0.22 −0.94 −0.39 0.98 0.72 k = C3; l = C1 i = C2 i = C4 c

c

c

c

c

c

a Values for the ﬁrst isostructural series (except Sm). b Values for the second isostructural series. c Not determined.

Despite this analysis of the observed LIS values, which led to a solution structure of these complexes of the CSAP (M) type, there is some conﬂicting evidence from the solution structure analysis of the other tertiary tetraamide complex [Eu(DOTTA)]3+, with a m/M isomer ratio of 2 (Aime et al., 1999b). Therefore we re-analyzed the 1 H LIS data, as well as the 13 C LIS data (R = Pr, Nd, Eu, excluding Sm) for the [R(L11 )]3+ complexes, ﬁrst through plots of para para δij /Sz j vs Cj /Sz j (eq. (48)) and δij /Cj vs Sz j /Cj (eq. (49)) (Ren et al., 2002), and using the H5 and H6 assignments of ﬁg. 41, which led to some re-assignments of the original data (Forsberg et al., 1995). Again breaks between light and heavy lanthanide ions were observed in most of those plots (see ﬁg. 47) reﬂecting variations of the contact Fi and pseudocontact B02 Gi parameters. Systematic deviations were also observed for Tm and Yb from the linear correlations deﬁned by the other R(III) ions within the second half of the series. The evaluated values of Fi and B02 Gi (and R 2 values) are shown in table 19. The LIS data were para para also plotted according to eq. (51), as δij /Sz j vs δkj /Sz j , eliminating the effect of any changes of B02 (ﬁg. 48a). These plots again show much less signiﬁcant breaks between light and heavy lanthanide ions than for the previous plots. The evaluated Rik and (Fi −Rik Fk ) parameters (and R 2 values) are shown in table 19. Again relative sensitivity of the nuclei to the breaks was H5, H6 H4 < H2, H3. Their values evaluated directly by eq. (51) and indirectly

430

C. PIGUET AND C.F.G.C. GERALDES

para

Fig. 47. Plots of δij /Sz j vs Cj /Sz j for H4 (F) and H6 (Q) of [R(L11 )]3+ (R = Ce–Yb, D2 O, pH = 7, adapted from Forsberg et al. (1995), Geraldes et al. (2003)).

using the Fi and B02 Gi values from eq. (48) (table 19) gave extremely good agreement for all the Rik ratios and only reasonably good for (Fi −Rik Fk ). Still, the breaks observed in the plots indicate that the Fi and Rik parameters change at the middle of the series, together with changes of B02 . para para para para Figure 48b shows 1 H LIS data plotted according to δij /δkj vs δlj /δkj (eq. (53)) for i = H3, H5 and H6, l = H1 and k = H4, which exhibit a break between the light (Pr–Eu) and the heavy lanthanide (Tb–Yb) complexes, thereby conﬁrming the changes of the proton Fi and/or Gi parameters at the middle of the series. Table 19 summarizes the α and β values calculated from the 1 H LIS data of the [R(L11)]3+ complexes for the light and heavy subseries of lanthanide ions. 3.2.4. [R(L12 –8H)]5− (L12 = 1,4,7,10-tetraazacyclododecane1,4,7,10-tetrakis(methylenephosphonic acid)) The 1 H, 13 C and 31 P LIS for the [R(L12 –8H)]5− complexes (except R = Pm, Gd) (where L12 –8H is DOTP8− , the tetrakis(methylenephosphonate) analog of DOTA, ﬁg. 40) have been reported at 298 K in D2 O at pH = 10 (Geraldes et al., 1992). Water 17 O NMR shift measurements of [Dy(L12–8H)]5− revealed that this complex lacks an inner-sphere water molecule (Ren and Sherry, 1996), which is in agreement with the crystal structure of the [Tm(L12– 8H)]5− complex (Paulus et al., 1995), where the coordination polyhedron of Tm is described as a twisted square antiprism (TSAP), m’, with the four ring nitrogens deﬁning one of its square faces and the four coordinated phosphonate oxygens deﬁning the other one. Structurally very similar to the [R(L10–4H)]− complexes, the methylene phosphonate arms of the

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

431

Table 19 Computed values for contact (Fi ), pseudo-contact (B02 Gi ) terms and R 2 values, according to eq. (48), comparison of Rik and (Fi −Rik Fk ) parameters calculated directly according to eq. (51), and α and β parameters calculated directly according to eq. (53), with those obtained from the above Fi and B02 Gi terms, for 1 H- and 13 C-nuclei in complexes [R(L11 )]3+ (R = Ce–Yb, D2 O, pH = 7, Forsberg et al. (1995), Ren et al. (2002), Geraldes et al. (2003)). The stom-numbering scheme is similar to that of ﬁg. 41 Compd R = Ce–Eua

Fi B02 Gi R2

Compd R = Tb–Ybb

Fi B02 Gi R2

Compd R = Ce–Eua

H1 −0.31 −1.43

Compd R = Ce–Eua

Compd R = Tb–Ybb

Compd R = Ce–Eua

Compd R = Tb–Ybb

H3 −1.56 0.62

H4 0.74 4.15

H5 −1.56 0.62

H6 −0.95 −1.08

0.999 H1 −4.06 −3.28

0.996 H2 0.05 1.17

0.977 H3 −0.62 0.90

0.998 H4 7.44 7.38

0.977 H5 −0.62 0.90

0.998 H6 −3.69 −2.58

0.706

0.790

0.744 C2 3.56 1.56

0.718

0.744

C1 4.25 3.59

0.704 C4 2.99 −2.54

0.978 C1

0.920 C2

Fi B02 Gi R2

Compd R = Tb–Ybb

H2 −1.18 0.80

C3 3.11 −2.44 0.992 C3

0.934 C4

Fi B02 Gi

c

c

c

c

c

c

c

c

R2

c

c

c

c

H2–H1 −0.65 −1.61 0.999 −0.56 −1.35 H2–H1 Rik (exp) −0.33 (Fi −Fk Rik )(exp) −1.20 R2 0.986 Rik (calc) −0.36 (Fi −Fk Rik )(calc) −1.51 Rik (exp) (Fi −Fk Rik )(exp) R2 Rik (calc) (Fi −Fk Rik )(calc)

α(exp) β(exp) R2

i = H2 14.09 4.94 0.934

α(exp) β(exp) R2

i = H2 1.40 0.78 0.90

H3–H1 −0.52 −1.95 0.998 −0.43 −1.69 H3–H1 −0.27 −1.66 0.994 −0.27 −1.72

a Values for the ﬁrst isostructural series (except Sm). b Values for the second isostructural series. c Not determined.

H4–H1 −2.97 −0.36 1.000 −2.90 −0.16 H4–H1 −2.27 −1.49 0.999 −2.25 −1.70

H5–H1 H6–H1 C2–C1 1.92 0.86 0.44 0.72 −0.42 1.62 1.000 1.000 0.980 −0.43 0.76 0.43 −1.69 −0.71 1.73 H5–H1 H6–H1 C2–C1 c 1.61 0.79 c 1.04 −0.49 c 1.000 1.000 c −0.27 0.79 c −1.72 −0.48 k = H4; l = H1 i = H3 i = H5 17.40 −0.35 6.01 −0.72 0.926 0.015 k = H4; l = H1 i = H3 i = H5 1.91 0.16 0.98 −0.64 0.832 1.000

C3–C1 C4–C1 −0.66 −0.66 5.75 5.55 0.940 0.840 −0.68 6.01 6.00 3.53 C3–C1 C4–C1 c

c

c

c

c

c

c

c

c

c

i = H6 8.01 2.42 0.94 i = H6 1.41 0.27 0.91

432

C. PIGUET AND C.F.G.C. GERALDES

(a)

(b)

para

para

para

para

Fig. 48. (a) Plots of δij /Sz j vs δkj /Sz j for the H3–H1 (2) and H4–H1 (F) pairs; (b) Plots of δij /δkj para para vs δlj /δkj for the Hi, H1, H4 triads (Hi = H3 (Q), H5 ("), H6 (F)) of [R(L11 )]3+ (R = Ce–Yb, D2 O, pH = 7, adapted from Geraldes et al. (2003)).

DOTP ligand are arranged in a propeller-like fashion above the basal plane made up of the four N donor atoms which encompass the R(III) ion, thereby generating a C4 symmetry axis in these complexes (ﬁg. 40). Four of the residual negative charges are localized on the phos-

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

433

phonate oxygen atoms, which are directed away from the lanthanide coordination site with the ﬁfth averaged over the bound oxygens in the coordination cage. These highly charged anionic complexes have four protonation steps over the pH range of 3–10, such that [R(L12 –7H)]4− is the predominant species at pH = 7.4, leading to signiﬁcantly pH dependent LIS values (Sherry et al., 1996). Thus, besides pH = 10, the LIS values at pH 7 and 3 were also analyzed. Unlike the DOTA complexes, only one set of resonances was observed in solution by 1 H, 13 C and 31 P NMR for the [R(L12–8H)]5− complexes, which thus exist in solution as racemic mixtures, M’ (square antiprism, SAP) ((δδδδ) and (λλλλ)) or m’ (twisted square antiprism, TSAP) ((δδδδ) and (λλλλ)) (ﬁg. 42), the two enantiomers of either case furnishing indistinguishable NMR signals at room temperature using conventional NMR techniques. Chiral NMR resolution, using the formation of diastereomeric adducts between the two enantiomers of [R(L12 –8H)]5− and a chiral substrate, has provided indirect, albeit conclusive, evidence for the existence of these two enantiomers. The ion-pair interactions between [R(L12 –8H)]5− and the chiral organic base, N-methyl-D-(-)glucamine (MEG), were investigated using 1 H, 13 C and 31 P NMR. Addition of MEG to a solution of [Eu(L12 –8H)]5− lifted the signal degeneracy of the NMR spectra, resulting in doubling of the corresponding signals (Aime et al., 1999c). Similar spectral resolution in the 1 H NMR spectrum of [Eu(L12–8H)]5− was achieved by the addition of the chiral transition metal complex, (+)− [Co(en)3 ]3+ (Sherry et al., 1996; Ren et al., 1997). The 1 H, 13 C and 31 P LIS data (pH = 10) were analysed by plotting the data for the [R(L12– para para 8H)]5− according to eq. (48), δij /Sz j vs Cj /Sz j , and eq. (49), δij /Cj vs Sz j /Cj (Geraldes et al., 1992). Breaks between light and heavy lanthanide ions were observed in those plots, reﬂecting variations of the contact Fi and pseudo-contact B02 Gi terms. Systematic deviations were also observed for Tm and Yb from the linear correlations deﬁned by the other R(III) ions within the second half of the series. These parameters were evaluated from those plots by subdivision of the lanthanides into two subgroups (Ce–Eu and Tb–Yb) and without such a subdivision (but excluding the Tm data). In the initial analysis, the B02 values were considered to be constant, and the Gi values, obtained without the lanthanide subdivision, were used together with distance ratios obtained from 1 H NMR T1 relaxation data. The geometric factors Gi for each nucleus were calculated from the minimized structure of [R(L12 –8H)]5− using a MMX force ﬁeld (average R–N and R–O bond lengths of 2.70 and 2.35 Å, respectively) and an axial symmetry model, as well as the R(III)-proton distance ratios. An optimum ﬁt of the LIS and relaxation data was obtained for a SAP conﬁguration, M’ (Geraldes et al., 1992), in disagreement with the later reported m’ single crystal structure of the [Tm(L12–8H)]5− complex (Paulus et al., 1995). However, in this NMR study the assignments of the H5 and H6 protons was opposite to the one adopted in the present review for all the tetraazamacrocyclic compounds (ﬁg. 41), and therefore their reassignments have to be made. With this reassignment, the 1 H and 13 C LIS data available for the [R(L12 –8H)]5− para complexes at pH = 10, 7 and 3 were reanalyzed (Ren et al., 2002). First, plots of δij /Sz j para vs Cj /Sz j (eq. (48)) and δij /Cj vs Sz j /Cj (eq. (49)) were obtained, giving breaks at Tb (ﬁg. 49), reﬂecting variations of Fi and B02 Gi . The values obtained from these plots are para para shown in table 20. Then plots according to eq. (51), δij /Sz j vs δkj /Sz j , again show

434

C. PIGUET AND C.F.G.C. GERALDES

para

Fig. 49. Plots of δij /Sz j vs Cj /Sz j for H1 (F) and H3 (Q) of [R(L12 –8H)]5− (R = Ce–Yb, D2 O, pH = 10, adapted from Ren et al. (2002)).

para

para

Fig. 50. Plots of δij /Sz j vs δkj /Sz j for the H3–H1 (2) and H4–H1 (Q) pairs of [R(L12 –8H)]5− (R = Ce– Yb, D2 O, pH = 10, adapted from Ren et al. (2002)).

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

435

Table 20 Computed values for contact (Fi ), pseudo-contact (B02 Gi ) terms and R 2 values, according to eq. (48), comparison of Rik and (Fi −Rik Fk ) parameters calculated directly according to eq. (51), and α and β parameters calculated directly according to eq. (53), with those obtained from the above Fi and B02 Gi terms, for 1 H, 13 C and 31 P-nuclei in complexes [R(L12 –8H)]5− (R = Ce–Yb, D2 O, pH = 10, Geraldes et al. (1992, 2003), Ren et al. (2002). The atom-numbering scheme is similar to that of ﬁg. 41 Compd R = Ce–Eua

H1

H2

H3

H4

H5

H6

Fi

−0.31

−0.44

−0.54

1.15

−0.36

−0.52

B02 Gi

−1.52

0.47

0.26

2.95

−1.13

−2.80

0.991

0.831

0.643

0.985

0.983

H1

H2

H3

H4

H5

H6

Fi

−1.19

0.29

−0.15

3.75

−1.30

−2.49

B02 Gi

−2.08

1.17

0.95

5.85

−1.65

−4.33

0.874

0.846

R2 Compd R = Tb–Ybb

R2

0.815

0.876

Compd R = Ce–Eua

C1

P

2.98

1.71

4.34

B02 Gi

2.28

0.92

−1.88

−1.06

R2

0.990

0.985

0.999

C2

C3

C1

P

−1.15

−2.16

3.71

1.00

−4.54

−4.59

0.817

0.760

3.91

B02 Gi R2

0.834

0.893

H2–H1 H3–H1 H4–H1 H5–H1 H6–H1 C2–C1 C3–C1 CP –C1 Rik (exp)

−0.34

−0.21

−1.86

0.73

1.05 −0.22 0.963 0.988

−0.82

1.84

0.41

0.03 0.994

1.35 0.995

4.97 0.999

−0.47 6.25 0.825

−0.54

−0.17

−1.94

0.74

1.84

0.40

−0.82

−0.46

(Fi −Fk Rik )(calc) −0.54

−0.61

0.57

−0.13

−0.01

1.34

4.98

6.22

Rik (calc) Compd

H2–H1 H3–H1 H4–H1 H5–H1 H6–H1 C2–C1 C3–C1 CP –C1 −0.54

−0.44

−2.76

0.79

2.08

0.28

−1.21

−1.18

(Fi −Fk Rik )(exp) −0.28

−0.62

0.65

−0.36

−0.01

0.71

3.51

2.10

Rik (exp) R2 Rik (calc)

0.992 0.993 0.998 −0.56 −0.46 −2.81

(Fi −Fk Rik )(calc) −0.19

−0.67

1.000 0.79 −0.36

0.47

1.000 0.28 −0.01

k = H4; l = H1 Compd R = Ce–Eua

0.796

1.85

Fi

(Fi −Fk Rik )(exp) −0.81 −0.91 0.795 0.715 R2

R = Tb–Ybb

0.812

C3

3.99

Compd R = Ce–Eua

0.814

C2

Fi

Compd R = Tb–Ybb

0.998

α(exp) β(exp) R2 α(calc) β(calc)

i = H2

i = H3

1.07 0.56

0.99 0.47

0.393 −2.21 −0.98

0.26 −1.55 −1.08

i = H6

1.25 −0.28

0.64 −0.05

0.29 −0.24

0.999 0.987 −1.22 −1.24

0.76

3.58

2.45

k = C2; l = C1

i = H5

0.977

0.995 0.27

0.925 2.15 0.09

i = C3 −2.42 4.04 0.997

i=P −2.15 4.12 0.981

−2.30 −2.29 3.68 4.62 continued on next page

436

C. PIGUET AND C.F.G.C. GERALDES Table 20, continued k = H4; l = H1 i = H2

Compd R = Tb–Ybb

k = C2; l = C1

i = H3

i = H5

i = H6

α(exp)

1.07

0.99

1.25

0.64

β(exp) R2

0.56 0.393

0.47 0.263

−0.28 0.977

−0.05 0.925

1.64 −0.88

1.95 0.09

α(calc) β(calc)

−3.15 −4.59

−3.22 −1.06

i = C3 −2.42 4.04 0.997 −2.45 4.57

i=P −2.15 4.12 0.981 −2.45 4.57

a Values for the ﬁrst isostructural series (except Sm). b Values for the second isostructural series.

less signiﬁcant breaks at Tb (ﬁg. 50). The calculated Rik and (Fi −Rik Fk ) parameters (and R 2 values) are also shown in table 20. Again, the relative sensitivity of the various nuclei to the breaks was: H5, H6 H4, C3 < H2, H3, C2 and P. The Rik and (Fi −Rik Fk ) parameters evaluated directly by eq. (51) and indirectly using the Fi and B02 Gi values from eq. (48) were compared (see table 20). The agreement is extremely good for all the Rik ratios and only reasonably good for (Fi −Rik Fk ). Again, the breaks observed in these plots indicate that the Fi and Rik parameters change at the middle of the series, together with changes of B02 . A previous analysis of the 1 H, 13 C and 31 P LIS data for the [R(L12–8H)]5− complexes within the second half of the series (R = Tb–Yb) using Reuben’s crystal-ﬁeld parameter independent method (Reuben, 1982) has come to the conclusion that these complexes are isostructural (Gi constant) and that Fi are invariant along the second half of the series (Ren and Sherry, 1996), showing that the deviations in the plots according to eqs. (48) and (49) (ﬁg. 49) in Tb–Yb, in particular for Tm and Yb, also reﬂect changes of B02 within this halfseries. Assuming that H4 has no contact shift contribution, Fi and RiH4 = Gi /GH4 values were obtained for i = C1, C2, CP and P nuclei, as well as the B02 values for the Tb–Yb complexes. The results have shown that B02 changes signiﬁcantly along the Tb–Yb half-series of complexes, with the largest value for Tm and the smallest for Yb (Ren and Sherry, 1996). para para para para Figure 51a shows the 13 C LIS data of C3 when plotted according to δij /δkj vs δlj /δkj (eq. (53)) for i = C3, l = C1 and k = C2, where all data points (n = 11) fall on a straight line. The 31 P LIS data when plotted in the same way (i = P, l = C1 and k = C2) also show a good linear relationship. Table 20 summarizes the α and β values obtained directly from these plots, which agree quite reasonably with those calculated from the Fi and B02 Gi parameters obtained from Reilley’s plots (table 20). However, like before, plots using other combinations give more or less pronounced breaks, such as for i = C4, l = C1 and k = C3, and for i = C2 or C3, l = C1 and k = C4 (Geraldes et al., 2003). This is again in agreement with the detected changes of Fi and Gi parameters at the middle of the R series and it illustrates the appearance of accidentally linear plots according to eq. (53). These conclusions are supported by plots of the 1 H LIS data according to eq. (53), obtained for i = H2, H3, H5 and H6, l = H1 and k = H4. While the plots are reasonably linear for i = H5 and H6 (ﬁg. 51b), they show large deviations from linearity for i = H2 and H3 (see table 21 for the α and β values).

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

437

(a)

(b)

para

para

para

para

Fig. 51. Plots of δij /δkj vs δlj /δkj (a) for the C3, C1, C2 triad; (b) for the Hi, H1, H4 triads (Hi = H5 (Q), H6 (")) of [R(L12 –8H)]5− (R = Ce–Yb, D2 O, pH = 7, adapted from Geraldes et al. (2003)).

3.2.5. Comparison of the structures of the [R(L10 –4H)]− , [R(L11 )]3+ and [R(L12 –8H)]5− complexes As described in the previous sections, the solution LIS data analysis for [R(L10 –4H)]− (M and m isomers), [R(L11)]3+ and [R(L12 –8H)]5− (pH = 10, 7 and 3) using the one nucleus, two nuclei and three nuclei methods gave quite comparable results. Their solution structures were systematically compared using the parameter data obtained from the last two graphical methods and listed in table 21 (Geraldes et al., 2003; Ren et al., 2002). In this table,

438

C. PIGUET AND C.F.G.C. GERALDES

Table 21 Comparison of the parameters for the 1 H LIS of the R-tetraazamacrocyclic complexes [R(L10 –4H)]− (M and m), [R(L11 )]3+ and [R(L12 –8H)]5− obtained using the graphical methods based on eqs. (51) and (53) (Ren et al., 2002; Geraldes et al., 2003) Compd. R = Ce–Eu [R(L12 –8H)]5− [R(L10 –4H)]− (M) [R(L10 –4H)]− (m) [R(L11 )]3+ R = Tb–Yb [R(L12 –8H)]5− [R(L10 –4H)]− (M) [R(L10 –4H)]− (m) [R(L11 )]3++ k = H4; l = H1 R = Ce–Eu [R(L12 –8H)]5− [R(L10 –4H)]− (M) [R(L10 –4H)]− (m) [R(L11 )]3+ R = Tb–Yb [R(L12 –8H)]5− [R(L10 –4H)]− (M) [R(L10 –4H)]− (m) [R(L11 )]3+

R21 F2 −R21 F1 R31 F3 −R31 F1 R41 F4 −R41 F1 R51 F5 −R51 F1 R61 F6 −R61 F1 −0.34 −0.27 −0.42 −0.65

−0.81 −0.62 −1.29 −1.61

−0.21 −1.00 −0.59 −0.52

−0.91 −1.89 −1.43 −1.95

−1.86 −3.56 −3.12 −2.97

1.05 −0.78 −0.90 −0.36

−0.54 −0.37 −0.37 −0.33

−0.28 −1.34 −1.24 −1.20 i = H2

−0.44 −0.44 −0.44 −0.27

−0.62 −2.76 −1.10 −2.56 −1.02 −2.57 −1.66 −2.27 i = H3 α β

0.65 −1.42 −0.85 −1.49

α

β

1.07

0.56

a

a

a

a

a

1.48 14.09

0.444 4.94

1.88 17.40

0.74 6.01

2.20 −0.35

1.07 3.11 0.86 1.40

0.56 1.28 0.60 0.78

0.99 2.17 1.54 1.91

0.47 0.97 0.80 0.98

1.25 0.80 −0.01 0.16

0.99

0.47

α 1.25

−0.22 0.22 −0.05 0.72

0.86 −0.93 0.86 0.86

0.79 −0.36 1.79 0.42 0.85 −0.23 1.61 1.04 i = H5 β

2.08 0.81 1.77 0.79

0.86 0.86 0.86 1.92

0.03 −2.60 −0.39 −0.42

−0.01 −0.84 −0.90 −0.49 i = H6 α β

−0.278

0.64

−0.05

a

a

a

0.22 −0.72

0.40 8.01

−0.12 2.42

−0.28 −0.37 −0.72 −0.64

0.64 3.00 1.25 1.41

−0.05 0.80 0.16 0.27

a Not determined.

ratios for the the Rik geometric ratios for the H1–H6 protons, relative to H1, and the Rik 12 5− C1–C4 carbons (C4 replaced by P atom in [R(L –8H)] ), relative to C1 are of high structural importance. The sign of Rik is different for the H1, H5 and H6 relative to H2, H3 and H4, and of C1 and C2 relative to C3 and C4(P), showing that these two groups of protons and carbon/phosphorus nuclei have distinct locations in the complexes relative to the dipolar shift cone deﬁned by 3 cos2 θ = 1. The absolute magnitude of the ring Rik ratios follow the order H4 > H1 > H2 > H3 for the [R(L11 )]3+ and [R(L12–8H)]5− complexes, and H4 > H1 > H3 > H2 for the M and m isomers of the [R(L10 –4H)]− complexes. The acetate proton ratios also differ signiﬁcantly, with H5 > H6 for the [R(L10 –4H)]− (M) and [R(L11)]3+ complexes, and H6 > H5 for the [R(L10 –4H)]− (m) and [R(L12 –8H)]5− complexes. Although the proton shifts of the [R(L12–8H)]5− complexes are signiﬁcantly pH dependent, with a decrease of the dipolar shifts when the pH drops from 10 to 3 (Ren et al., 2002), the four protonation steps undergone by the phosphonate groups at their unbound oxygens does not cause a variation of the complex geometry, as the Rik are nearly invariant from pH = 10 to pH = 3 (< ±4%). Such large decreases of dipolar shifts with pH decrease are attributed to a decrease of the crystal ﬁeld parameter B02 upon protonation. As described before,

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

439

the B02 values for the Tb–Yb complexes of [R(L12 –8H)]5− have been obtained assuming that H4 has no contact shift contribution, showing that B02 changes signiﬁcantly along the Tb– Yb half-series of complexes, with the largest value for Tm and the smallest for Yb (Ren and Sherry, 1996). However, these quantitative values must be seen with some caution, as the assumption that FH4 is negligible for the [R(L12 –8H)]5− complexes is doubtful (see table 20). On the other hand, calculation of B02 ratios, B02 (R = Ce−Eu) B02 (R = Dy−Yb)

,

which is obtained by assuming constant Gi values along the series and taking the slope of a linear plot of B02 Gi (R = Ce–Tb) vs B02 Gi (R = Ce–Tb), could not be undertaken, since in the present systems Gi values display only small changes along the R(III) series. Comparing the experimental and calculated Rik values for each proton in the four complexes studied (table 22), in particular for the two isomers, M and m, of [R(L10–4H)]− , which result from different arrangements of the four pendant arms around the R(III) ion, one concludes that these ratios are quite constant for the ring protons in all complexes, in accordance with very similar macrocyclic ring conformations. The differences between M and m forms occur in the H5 and H6 protons of the pendant arms, with very good agreement of experimental and calculated data for the [R(L10–4H)]− complexes (also with the X-ray results) and for the [R(L11)]3+ complexes, where the calculated structure is M (Forsberg et al., 1995). For the [R(L12 –8H)]5− complexes, the re-assignment of these protons indicates that they have a m’ solution conformation, in agreement with calculated values for models of the M’ and m’ conformations and with the X-ray crystal structure. Further information about the structure of these macrocyclic complexes is provided in table 23, which compares the experimental Yb–H distances normalized to H1 (rHi /rH1 ) obTable 22 Comparison of experimental and calculated geometric ratios Rk1 = Gk /GH1 for H1–H6 protons of [R(L10 –4H)]− (M and m), [R(L11 )]3+ and [R(L12 –8H)]5− [R(L10 –4H)]− (M) [R(L10 –4H)]− (m) [R(L11 )]3+ [R(L12 –8H)]5− (M’) (m’)

Exp.a Calc.a Exp.a Calc.a Exp.b Calc.b Exp.c Calc.d Calc.d

H1 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

H2 −0.31 −0.41 −0.37 −0.26 −0.33 −0.35 −0.54 −0.65 −0.63

H3 −0.44 −0.45 −0.44 −0.29 −0.27 −0.27 −0.44 −0.51 −0.46

H4 −2.56 −2.73 −2.57 −2.26 −2.27 −2.29 −2.76 −3.15 −2.89

H5 1.79 1.82 0.85 0.89 1.61 1.65 0.79 2.29 0.87

H6 0.81 0.86 1.77 1.63 0.79 0.79 2.08 0.92 2.41

a Aime et al. (1992b). b Forsberg et al. (1995). c Geraldes et al. (1992). d Calculated for models of M’ and m’ structures (Ren et al., 2002). The m’ structure was obtained based on the crystal structure of [Tm(L12 –8H)]5− and the M’ structure by changing m’ to give a twist angle of +39◦ .

440

C. PIGUET AND C.F.G.C. GERALDES

Table 23 Comparison of experimental and calculated Yb–Hi distance ratios relative to H1, rHi /rH1 , for H1–H6 protons of [R(L10 –4H)]− (M and m), [R(L11 )]3+ and [R(L12 –8H)]5− [R(L10 –4H)]− (M) [R(L10 –4H)]− (m) [R(L11 )]3+ [R(L12 –8H)]5− (M’) (m’)

Exp.a Calc.a Exp.a Calc.a Exp.b Calc.b Exp.c Calc.d Calc.d

H1 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

H2 1.19 1.17 1.17 1.17 1.13 1.19 1.16 1.19 1.21

H3 1.21 1.17 1.19 1.17 1.13 1.19 1.16 1.19 1.21

H4 0.96 0.99 0.95 0.99 0.90 0.99 0.95 1.01 1.04

H5 1.04 0.99 1.02 0.99 1.01 0.98 1.22 0.96 1.18

H6 1.16 1.15 1.05 0.98 1.19 1.16 0.98 1.17 0.93

a Aime et al. (1992b). b Forsberg et al. (1995). c Geraldes et al. (1992). d Calculated for models of M’ and m’ structures (Ren et al., 2002).

tained using the proton T1 relaxation times from the literature and eq. (18), with the relative distances calculated for the M and m/m’ forms of the [R(L10 –4H)]− complexes and the M form of the [R(L11)]3+ complex. There is no signiﬁcant differences in the relative distances of the ring protons for all these Yb complexes, which also agree with the calculated values. Due to the different arrangements of the pendant acetate arms around the Yb ion, the calculated Yb–H distances of H5 and H6 in the M and m/m’ forms differ quite substantially: while H5 is closer to Yb than H6 in M, their distances to Yb are about the same in m/m’. The experimental results for the [R(L10 –4H)]− M and m/m’ isomers agree very well with the predicted values, and the experimental results for the [R(L11)]3+ complex is consistent with a M form in solution. In the case of [R(L12–8H)]5− , the experimental data also agrees with the values calculated for a m’ form (Ren et al., 2002). Finally it is worth noting that a comparison of the α and β values, obtained from plots of the 1 H LIS for the acetate protons in the three complexes according to eq. (53), for i = H5 and H6, with l = H1 and k = H4 (table 21), is not indicative of their structure being either SAP (M) or TSAP (m or m’), despite these structures only differ in the arrangement of the pendant arms around the metal ion. Those α and β parameters do not reﬂect those structural changes directly, probably as a result of their very indirect structural dependence on the RiH4 (i = H5 and H6) geometric ratio (eq. (53)), which is mixed with dependence on the RH1H4 geometric ratio and hyperﬁne coupling constants ratios SiH4 and SH1H4 , which signiﬁcantly change for the various complexes (table 21). This reduces the structural diagnostic power of the three nuclei method based on eq. (53). 3.2.6. [R(L13 –2H)2]− (L13 = phtalocyanine) Considerable interest has been focused on the physico-chemical properties of sandwich complexes of lanthanide(III) ions with two macrocyclic conjugated rings such as phtalocyanine. Several X-ray crystallographic studies on Nd(III) (Kasuga et al., 1980) and Lu(III) (Mous-

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

441

Fig. 52. The structure of [R(L13 –2H)2 ]− , with the twist angle α, α = 45◦ for the D4d form, and 0◦ for the D4h form (adapted from Konami et al. (1989)).

savi et al., 1988) complexes have been carried out for H[Nd(L13–2H)2 ], [N(n Bu)4 ][Lu(L13– 2H)2 ] and H[Lu(L13–2H)2 ]. These reveal quite similar solid-state structures, where the R(III) cation is 8-coordinated by the isoindole nitrogen atoms of the two phtalocyanine rings in quasi square antiprismatic geometries (D4d symmetry), with staggering angles α between the two stacked phtalocyanines (ﬁg. 52) of 45◦ , 43◦ and 41◦ , respectively. The benzimidazole groups are somewhat tilted, giving a slightly bowl-type deformation of the phtalocyanine macrocycles towards the lanthanide ion. Slight distortions of some of these sandwich structures, with small deviations of the mean planes of the two phtalocyanines from parallel positions, were assigned to ion packing in the crystals. The proton NMR spectra of the [N(n Bu)4 ][R(L13–2H)2] (R = Pr–Lu except Pm, Gd) complexes in CD3 CN solution at room temperature are very simple in the aromatic region, with only one H1 and one H2 resonance of the phtalocyanine rings, indicating that the complexes have a C4 axis in solution (Konami et al., 1989). This is compatible with a D4h square prismatic or a D4d square antiprismatic geometry, depending whether the two stacked phtalocyanines are eclipsed or staggered, or fast interconversion between the two. The splitting of the Q band observed in the UV-vis absorption spectra of the R = Pr, Lu complexes in CD3 CN solution excludes the D4h structure. From the LIS values of the H1 and H2 protons in the parapara para magnetic complexes, plots of δij /Sz j vs Cj /Sz j (eq. (48)) and δij /Cj vs Sz j /Cj (eq. (49)) were obtained, which showed breaks near the middle of the lanthanide series and also signiﬁcant deviations from linearity within each of the two subfamilies of lanthanides, reﬂecting variations of the coupling constant Fi and the pseudo-contact term B02 Gi (ﬁg. 53a and table 24). In the original work, B02 Gi values were identiﬁed with Gi and single Fi and Gi values were obtained for H1 and H2 along the lanthanide series which did not fully agree with our analysis (table 24, Konami et al. (1989)). Fitting of the geometrical dependence of the experimentally derived Rik ratios to a chemical model of the [R(L13–2H)2 ]− complexes based on the crystal structures of the Nd and Lu compounds gave an average distance between the two rings in the sandwich compound of 2.54 Å and an average R–N distance of 2.31 Å (Konami et al., 1989). However, the data analysis available does not prove isostructurality in solution. para para A plot of δij /Sz j vs δkj /Sz j (eq. (51)) for i = H2 and j = H1, according to the two-nuclei crystal-ﬁeld independent technique, which eliminates the effect of any changes

442

C. PIGUET AND C.F.G.C. GERALDES

(a)

(b)

para

para

para

Fig. 53. (a) Plots of δij /Sz j vs Cj /Sz j for H1 (F) and H2 (2) and (b) plot of δij /Sz j vs δkj /Sz j for the H1–H2 (F) pair in [R(L13 –2H)2 ]− (R = Pr–Yb, CD3 CN, adapted from Konami et al. (1989), Geraldes et al. (2003)).

in B02 , gives a single straight line along the lanthanide series (ﬁg. 53b), conﬁrming that the complexes are isostructural and that the B02 parameter and Fi change along the series. There is generally a good agreement between experimental and calculated Rik and (Fi −Fk Rik ) parameters (table 24).

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

443

Table 24 Computed values for contact (Fi ), pseudo-contact (B02 Gi ) terms and R 2 values, according to eq. (48) and comparison of Rik and (Fi −Rik Fk ) parameters calculated directly according to eq. (51) with those obtained from the above Fi and B02 Gi terms, for 1 H-nuclei in complexes [R(L13 –2H)2 ]− (R = Pr–Yb, CD3 CN, Konami et al. (1989), Geraldes et al. (2003)). See ﬁg. 52 for the atom-numbering scheme Parameter Fi B02 Gi

Compd R = Pr–Eua

H1 0.34 0.09

R2

Compd R = Tb–Ybb

0.380 0.426 H2–H1 0.52 0.01 0.994 0.67 −0.07

Compd R = Pr–Eua

Rik (exp) (Fi −Fk Rik )(exp) R2 Rik (calc) (Fi −Fk Rik )(calc)

H2 0.16 0.06

Compd R = Tb–Ybb

H1 0.59 0.23

H2 0.33 0.11

0.649 0.652 H2–H1 0.48 0.02 0.994 0.48 0.05

Compd R = Pr–Yb

Compd R = Pr–Yb

H1 0.44 0.22

H2 0.24 0.11

0.601 0.600 H2–H1 0.49 0.03 0.993 0.50 0.02

a Values for the ﬁrst isostructural series (except Sm). b Values for the second isostructural series.

4. Application of the model-free methods to axial bimetallic lanthanide complexes with sterically rigid ligands Axial symmetry according to Bleaney’s approach is maintained in polymetallic lanthanide complexes when the metals lie on the molecular threefold or fourfold axes. For n magnetically non-coupled lanthanide ions packed along the symmetry axis, contact and pseudo-contact contributions can be considered as additive and the original model-free equation (eq. (47)) is transformed into eq. (61) in which the sum runs over the n paramagnetic centres, each being located at the origin of its own reference frame associated with a speciﬁc set of axial coordinates θim and rim (the z axis corresponds to the molecular symmetry axis, ﬁg. 54), para

δij

pc

= δijc + δij =

n

m 2m m Fim Sz m j + Cj B0 Gi .

(61)

m=1

For homopolymetallic axial complexes, the spin expectation values and Bleaney’s factors are m identical for all metallic sites (Sz m j = Sz j and Cj = Cj ) and can be factorized out to give eq. (62) which can be linearized according to the method proposed by Reilley et al. (1975) for monometallic complexes (eqs. (63), (64), Elhabiri et al. (1999)), n n m para m 2 m δij = (62) Fi Sz j + B0 Gi Cj , para δij

Sz j

=

para

δij

Cj

m=1 n

=

m=1 n

Fim

+

m B02 Gm i

m=1

m=1 n

m B02 Gm i

m=1

+

n m=1

Fim

Cj , Sz j

Sz j . Cj

(63)

(64)

444

C. PIGUET AND C.F.G.C. GERALDES

Fig. 54. Axial coordinates considered in bimetallic axial lanthanide complexes (adapted from Rigault et al. (2000a)).

The derivation of a general crystal-ﬁeld independent method for polymetallic lanthanide complexes related to eq. (51) is precluded by the consideration of variable numbers of different crystal-ﬁeld parameters (maximum n) depending on the exact symmetry of the axial complex (see sect. 4.1.1, Rigault et al. (2000a)). 4.1. Complexes with threefold symmetry 4.1.1. [R 2 (L14 –2H)3] (L14 = bis{1-ethyl-2-[6’-carboxy)pyridin-2’-yl] benzimidazol-5-yl}methane) Reaction of the bis-tridentate receptor [L14–2H]2− with R(ClO4 )3 in water produces the highly stable homobimetallic triple-stranded helicates [R 2 (L14–2H)3 ] (R = La–Tb except Pm and R = Er–Yb–Lu, log β[R2 (L14 –2H)3] = 51(4), Elhabiri et al. (1999)). 1 H NMR spectra point to rigid D3 -symmetrical complexes for which exchange between the helical enantiomers is slow on the NMR time scale (i.e., the methylene protons of the ethyl residues are systematically diastereotopic, ﬁg. 55). The considerable intermetallic separation (8.81–8.83 Å in the crystal structures of [Eu2 (L14–2H)3 ] and [Tb2 (L14 –2H)3]) prevents magnetic coupling and the ‘isolating’ methylene spacer separating the two tridentate units restrict through-bond contact interactions for a given nucleus i to a single paramagnetic centre. Under these conditions and for D3 1 2 symmetrical bimetallic lanthanide complexes (i.e., B02 = B02 = B02 ), eqs. (62)–(64) simplify to eqs. (65)–(67)

para δij = Fi Sz j + B02 G1i + G2i Cj , (65)

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

445

Fig. 55. Schematic formation of the D3 -symmetrical complexes [R 2 (L14 –2H)3 ] in water with numbering scheme. The representation of [R 2 (L14 –2H)3 ] corresponds to the crystal structure of [Eu2 (L14 –2H)3 ](H2 O)20.5 (Elhabiri et al., 1999).

Table 25 Computed values for contact (Fi ), pseudo-contact (B02 (G1i + G2i )) terms and agreement factors (AFi ) for 1 H-nuclei in complexes [R 2 (L14 –2H)3 ] (D2 O, 298 K, Elhabiri et al. (1999)). See ﬁg. 55 for the atom-numbering scheme Compd R = Ce–Tb

H1 Fi 0.32(4) B02 (G1i + G2i ) −0.38(3) 0.03 AFi −0.47(2) Fi B02 (G1i + G2i ) −0.41(6) 0.20 AFi

R = Er–Yb

H2 0.21(4) −0.32(1) 0.04 −0.15(3) −0.30(4) 0.18

H3 0.36(5) −0.35(2) 0.08 −0.46(2) −0.42(7) 0.19

H4 0.13(1) −0.05(3) 0.04 0.07(3) 0.058(9) 0.08

H5 0.011(2) 0.032(8) 0.06 0.07(5) −0.004(9) 0.04

H6 −1.7(2) 0.76(7) 0.35 1.99(2) 2.07(4) 0.002

H7 −0.02(1) 0.086(4) 0.11 −0.11(4) 0.11(1) 0.06

para

Cj = Fi + B02 G1i + G2i , Sz j Sz j δij

para

δij

Cj

(66)

Sz j = B02 G1i + G2i + Fi . Cj para

(67) para

Plots of δij /Sz j vs Cj /Sz j (eq. (66)) and δij /Cj vs Sz j /Cj (eq. (67)) for the 1 H NMR data of [R 2 (L14–2H)3 ] (R = Ce–Tb except Pm and R = Er–Yb) display an abrupt deviation from linearity between R = Tb and R = Er and require two different straight lines (ﬁg. 56). Two different isostructural series have been considered for R = Ce–Tb and Er–Yb, and two sets of contact Fi and pseudo-contact B02 (G1i + G2i ) terms are obtained according to least-squares ﬁts of eq. (65) (table 25, Elhabiri et al. (1999)).

446

C. PIGUET AND C.F.G.C. GERALDES

para

para

Fig. 56. Plots of (a) δij /Sz j vs Cj /Sz j (eq. (66)) and (b) δij /Cj vs Sz j /Cj (eq. (67)) for H6 in [R 2 (L14 – 2H)3 ] (R = Ce–Eu, Er–Yb, D2 O, 298 K, adapted from Rigault et al. (2000a)).

The crystal-ﬁeld parameter B02 can be removed when eq. (65) is expressed for two different nuclei i and k (Rigault et al., 2000a). The resulting crystal-ﬁeld independent eq. (68) is very similar to eq. (51) except that global geometrical factors (G1i + G2i ) replace Gi . para (G1i + G2i ) δkj (G1 + G2i ) + · = Fi − Fk i1 . Sz j (Gk + G2k ) (G1k + G2k ) Sz j para

δij

para

para

(68)

Plots of δij /Sz j vs δkj /Sz j (eq. (68)) for the various pairs of paramagnetic NMR shifts in [R 2 (L14 –2H)3] show three different behaviours depending on the protons involved (ﬁg. 57, Rigault et al. (2000a)). Firstly, no obvious correlation is observed for pairs involving H5 which can be explained by the peculiar location of this proton in the triple-stranded helicate. According to the D3 -averaged crystal-structure of [Eu2 (L14–2H)3 ], the axial coordinates amount to 1 = 54.1 ◦ and θ 2 = 55.0 ◦ which are both close to the magic angle (54.7 ◦ ) and lead to a draθH5 H5 matic sensitivity to faint structural changes along the lanthanide series as similarly observed for H11 in [RCo(L5)3 ]6+ (see sect. 3.1.5) and C4 in [R(L3 )3 ]3+ (see sect. 3.1.3). Nevertheless, this observation points to possible minor geometrical changes from one lanthanide to the other, but it is not diagnostic for signiﬁcant structural variations occurring along the lanthanide series. Secondly, pairs involving protons H1-3,6,7 display a single straight line for the complete lanthanide series (Ce–Yb, ﬁg. 57a) which indicates that (i) no signiﬁcant structural variation occurs along the complete lanthanide series and (ii) changes in the crystal ﬁeld parameters affect the linearity of the one-nucleus methods. Thirdly, related plots according to eq. (68) involving H4 clearly exhibit two straight lines, one for the large (Ce–Tb) and one for the small (Er–Yb) lanthanide ions with an abrupt transition between them (ﬁg. 57b). This behaviour contrasts with that observed for H1-3,6,7 and apparently leads to opposite conclusions in which two different structural arrangements should be invoked. However, both metallic centres signiﬁcantly contribute to the paramagnetic shift

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

para

447

para

Fig. 57. Crystal-ﬁeld independent plots of (a) δij /Sz j vs δkj /Sz j (eq. (68)) for the H2–H3 and (b) H2–H4 pairs in [R 2 (L14 –2H)3 ] (R = Ce–Tb, Er–Yb, D2 O, 298 K, adapted from Rigault et al. (2000a)).

i angles (i = 1, 2) are distributed on both sides of the of H4 (G1H4/G2H4 = 0.58) and the θH4 magic angles (49.1◦ and 63.0◦ according to the crystal structure of [Eu2(L14 –2H)3]). The paramagnetic shift of H4 is thus particularly sensitive to minor structural variations as a result of its peculiar geometrical location. Theoretical computed Rik factors obtained when the R · · · R distance is increased by stepwise increment of ≈ 0.2 Å from 8.4 Å to 9.2 Å indeed show small variations for Hi–Hk pairs (i = k and i, k = 1, 2, 3, 6, 7), but Hi–H4 pairs (i = 4) exhibit drastic changes which conﬁrm their extreme sensitivity to minor structural changes (ﬁg. 58).

Fig. 58. Computed Rik factors for pairs H3Hk (k = 1, 2, 4, 6, 7) in the crystal structure of [Eu2 (L14 –2H)3 ] (the intermetallic distance d varies from 8.4 to 9.2 Å, adapted from Rigault et al. (2000a)).

448

C. PIGUET AND C.F.G.C. GERALDES

The Rik factors found in solution are in good agreement with those calculated from the averaged D3 -symmetrical crystal structure leading to an agreement factor AF = 0.17, and to the conclusion that the crystal structure of [Eu2 (L14–2H)3 ] is a satisfying model for the complexes in solution along the complete lanthanide series. The breaks observed according to the one-nucleus methods (eqs. (66), (67), ﬁg. 56) have been assigned to concomitant changes of Fi and B02 occurring between R = Tb and R = Er, but the minor variation of the slopes for para the two straight lines obtained for δij /Sz j vs Cj /Sz j plots (eq. (66), ﬁg. 56a) suggests a ratio of crystal-ﬁeld parameters close to unity (Rigault et al., 2000a). A plot of B02 (G1i + G2i )R=Ce−Tb vs B02 (G1i + G2i )R=Er−Yb excluding H5 gives a rough linear correlation with B02 (R = Ce–Tb) B02 (R = Er–Yb)

= 0.8(2).

Finally, global geometrical factors G1i + G2i calculated from the crystal structure of [Eu2(L14 – j 2H)3 ] have been used for estimating magnetic anisotropies χzz − (1/3) Tr χ j with eq. (69) and using four contact contributions δijc (i = H1, H2, H3, H6, Elhabiri et al. (1999)). Since only j

three protons display no contact contribution, only rough estimations of χzz − (1/3) Tr χ j are obtained and no comparison with Bleaney’s factors has been performed,

1 1 1 para j c j 2 δij = δij + (69) χzz − Tr χ G i + Gi . 2NA 3 Isostructurality along the complete lanthanide series has been ultimately conﬁrmed by relaxation measurements. For the bimetallic complexes [R 2 (L14 –2H)3], each nucleus undergoes the sum of two dipolar and two Curie-spin paramagnetic contributions to their longitudinal relaxation rate. Thus eq. (18) is no longer valid and must be replaced with eq. (70) which takes into account the effect of the two paramagnetic centres (ﬁg. 54, Elhabiri et al. (1999)), 1 6 para 2 )6 (r 1 )6 · (r 2 )6 T1i (rref ) + (rref i i (70) · . = para 1 )6 · (r 2 )6 T1ref (ri1 )6 + (ri2 )6 (rref ref Taking the rin distances observed in the crystal structure of [Eu2(L14 –2H)3] and H3 as an internal reference, the calculated ratios 1 6 2 )6 (r 1 )6 · (r 2 )6 (rref ) + (rref i i · 1 )6 · (r 2 )6 (ri1 )6 + (ri2 )6 (rref ref para

para

closely match the experimental terms T1i /T1ref obtained for R = Ce, Pr, Nd, Yb, henceforth conﬁrming that [Eu2 (L14 –2H)3] is a satisfying structural model. 4.2. Complexes with fourfold symmetry 4.2.1. [R 2 (L15 –2H)3] (L15 = octaethylporphyrin) Early efforts in the synthesis and characterisation of lanthanide(III) porphyrin coordination compounds led to monoporphyrinates such as [R(TPP)(acac)(H2O)2 ] (where (TPP)2−

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

449

Fig. 59. Conﬁgurations of (A) mono-tetrapyrroles [R(L15 – 2H)LL’L”L”’], (B) bis-tetrapyrroles [R(L15 –2H)2 ] and (C) tris-tetrapyrroles [R 2 (L15 –2H)3 ] (adapted from Buchler et al. (1986)).

is 5,10,15,20-tetraphenylporphyrin and H(acac) is acetylacetone) representing coordination type A of square antiprismatic geometry (ﬁg. 59) (Wong et al., 1974; Wong and Horrocks, 1975). A protonated bis-porphyrinate, H[Pr(TTP)2], was also obtained but could not be crystallised and characterised structurally (Buchler et al., 1983). However, the use of octaethylporphyrin ([L15–2H]2− or (OEP)2− ) afforded the entire series of double-decker sandwich compounds [R(L15 –2H)2] (R = La–Lu except Pm) (coordination type B) and triple-decker dimetallic compounds [R 2 (L15 –2H)3] (R = La–Gd except Pm) (coordination type C) of square antiprismatic geometry (ﬁg. 59) (Buchler et al., 1986). The crystal structures of the Ce compounds of both series, [Ce(L15–2H)2 ] and [Ce2 (L15 – 2H)3 ], were obtained by X-ray crystallography. In the ﬁrst compound, the Ce(IV) ion has a square antiprismatic coordination polyhedron formed by the eight nitrogen atoms of the two staggered porphyrin rings, with rotational angle α = 41.8◦ (ﬁg. 60a). The crystal structure of the dimetallic compound [Ce2 (L15 –2H)3] consists of a small stack of three ligand dianions separated by two Ce(III) ions, which deﬁne a C4 symmetry axis. Due to the presence of an inversion center located between the two Ce(III) ions, the two external rings have the same orientation with respect to the internal macrocycle. Each ion is surrounded by eight nitrogen atoms, four of which belonging to the external and four to the internal porphyrinate ring. The coordination polyhedron is more distorted from the ideal square antiprism than in the monometallic compound, as the mean rotational angle of the two macrocycles is α = 24.5◦ (ﬁg. 60b). Furthermore, the Ce(III) ions are closer to the 4Np mean planes of the external rings (1.394 Å) than of the internal ring (1.876 Å) and the 4Np mean-plane separation is

Fig. 60. Stick bond model projection of [Ce(L15 –2H)2 ] (A) and [Ce2 (L15 –2H)3 ] (B), showing the respective relative rotations of the different macrocyclic units (adapted from Buchler et al. (1986)).

450

C. PIGUET AND C.F.G.C. GERALDES

approximately 3.27 Å (Buchler et al., 1986). There is also a strong C4v doming of the outer rings, which also helps to relax inter-ring alkyl crowding. The 1 H NMR spectra of the dimetallic compounds [R 2 (L15 –2H)3] (R = La–Eu except Pm) were reported in CCl4 at 293 K (Buchler et al., 1986, 1988, 1989), while the 13 C NMR spectra of the corresponding R = La, Ce and Pr compounds were recorded in CCl4 /CD2 Cl2 or CCl4 /C6 D6 mixtures (Buchler et al., 1992). The LIS values of the methyl (CH3 ), methylene (CH2 ) and methine (CH) proton resonances of the outer- and inner rings were obtained for the paramagnetic complexes, relative to the diamagnetic La complex. Since the outer rings do not possess a symmetry plane, the outer ring CH2 protons are diastereotopic and two resonances result. As all nuclei of these complexes experience additive LIS effects from the two paramagnetic centers, which have negligible electron spin interactions between them, it is not surprising that the relative LIS values were larger for all the protons of the inner ring, which experience the closer magnetic inﬂuence of the two paramagnetic centers. In a structural analysis of the observed proton LIS values for the Ce(III) dimetallic complex, the contact contribution was neglected (Buchler et al., 1989). Axial dipolar contributions from the two Ce ions were added using eq. (65) which reduces to eqs. (71), (72) for the outer ring and inner ring protons, respectively (Ce(1) is proximal to and Ce(2) is distal to the outer ring)

para dip,Ce(1) dip,Ce(2) δij = δij (71) + δij = B02 G1i + G2i Cj , para

δij

dip,Ce(1)

= 2δij

dip,Ce(1)

= 2B02 G1i Cj .

dip,Ce(2)

(72)

> δij , the inner ring dipolar shifts are larger than those of the outer ring. As δij A solution geometry for [Ce2 (L15 –2H)3] was searched for which there was a reasonable agreement between experimental dipolar shift ratios and calculated geometric factor ratios, using as geometrical model the single crystal structure of the compound. The degree of doming of the outer rings and the outer Ce positions were increased systematically, as well as alkyl group bond rotation. The geometric factors were calculated for the protons and used in the solution structural search. This procedure gave compelling evidence for inter-ring steric crowding and subsequent limited rotation of the outer ring alkyl groups such that the outer β-CH3 groups stay far away from the inner ring alkyl groups to minimize inter-ring steric crowding. We proceeded to verify if the approximation of neglecting the contact contribution to the 1 H para para LIS values is warranted. Plots of δij /Sz j vs Cj /Sz j (eq. (66)) and δij /Cj vs Sz j /Cj (eq. (67)) for the 1 H NMR data of [R 2 (L15 –2H)3] (R = Ce, Pr, Nd, Eu) do not give very good linear correlations (ﬁg. 61a). The irregularities are possibly due to deviations of the relative dipolar shift values from relative Bleaney’s constants Cj , in particular for the Ce and Pr ions and inner-ring protons, as observed before (Buchler et al., 1992). The contact Fi and pseudocontact B02 (G1i + G2i ) terms, obtained according to least-squares ﬁts of eq. (65), indicate that some of the protons do have non-negligible contact shifts (table 26). para para All the plots of δij /Sz j vs δkj /Sz j (eq. (68)) for the various pairs of proton LIS values of [R 2 (L15–2H)3] give good linear correlations (ﬁg. 61b) indicating that the complexes are isostructural and that the irregularities of the LIS values are due to changes of the crystal ﬁeld

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

451

(a)

(b)

para

para

para

Fig. 61. Plots of (a) δij /Sz j vs Cj /Sz j for CH(i) (2) and CH(o) (F); (b) δij /Sz j vs δkj /Sz j for the para para para para CH3(o) –CH(i) (F) and CH3(i) –CH(i) (2) pairs; (c) δij /δkj vs δlj /δkj for the CH3(i) –CH2(i) –CH(i) (2) and CH3(o) –CH2(i) –CH(i) (Q) triads (data for the complexes [R 2 (L15 –2H)3 ] (R = Ce–Eu), CCl4 , 293 K, adapted from Buchler et al. (1992), Geraldes et al. (2003)).

parameter B02 . However, the agreement of experimental and calculated Rik and (Fi −Fk Rik ) parameters is not always good, in particular for the CH2 protons (table 26). All the calculated geometric terms Gi have the same sign except the outer-ring CH3 protons (outside the dipolar cone). The Rik values obtained by the above method give very good agreement with para para the calculated geometric factors (Buchler et al., 1989) except for CH2(i) . Plots of δij /δkj vs

452

C. PIGUET AND C.F.G.C. GERALDES

(c)

Fig. 61. Continued.

para

para

δlj /δkj (eq. (53)) according to the three nuclei method are also affected by the irregularities of the dipolar shifts found in the Reilley method (ﬁg. 61c and table 26). The 13 C NMR spectra of the [R 2 (L15 –2H)3] (R = La, Ce, Pr) complexes were obtained in a CCl4 /CD2 Cl2 mixture, yielding 13 C LIS values for the α, β, methine (CH), methylene (CH2 ) and methyl (CH3 ) carbons of the inner and outer rings (Buchler et al., 1992). 13 C LIS values in aromatic systems can have three contributions: para

δij

MCdip

= δijc + δij

LCdip

+ δij

(73)

,

where the presence of a signiﬁcant contact shift, δijc , reﬂects spin density delocalization onto LCdip

the porphyrin carbon atoms, leading to a ligand-centered dipolar shift, δij MCdip MCdip ditional metal-centered dipolar shift, δij . The δij

, besides the tra-

term is the easiest to estimate assuming axial magnetic symmetry (a) the geometric terms from the solution geometry established above (Buchler et al. (1989) were used) (b) the magnetic anisotropy for the Ce(III) complex was obtained from plots of the proton LIS values, assumed to be purely metal-centered dipolar, versus the respective geometric terms, yielding (χ − χ⊥ ) = 2980 × 10−6 cm3 · mol−1 MCdip per Ce, which is then valid for the 13 C LIS. Comparison of the calculated δij values with the observed LIS shows very good qualitative agreement, except for the α-carbon nuclei, the closest to the Ce ions, in particular for the outer rings. This is indicative of the presence of contact shifts and ligand-centered dipolar shifts, from direct 4f orbital overlap and/or indirect spin polarization of the 6s or 6p orbitals involving a low-lying (π or π ∗ ) porphyrin molecular orbital. However separation of the contact and ligand-centered dipolar contributions was not possible (Buchler et al., 1992).

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

453

Table 26 Computed values for contact (Fi ), pseudo-contact (B02 (G1i + G2i )) terms and R 2 values, according to eq. (65) and comparison of Rik and (Fi −Rik Fk ) parameters calculated directly according to eq. (68) with those obtained from the above Fi and B02 (G1i + G2i ) terms, for 1 H-nuclei in complexes [R 2 (L15 –2H)3 ] (R = Ce–Eu, CCl4 , 293 K, Buchler et al. (1992), Geraldes et al. (2003))a Compd R = Ce–Eub

Compd R = Ce–Eub

Compd R = Ce–Eub

Compd R = Ce–Eub

CH3(o) Fi −0.18 B02 (G1i + G2i ) 0.10

CH3(i) −0.75 1.18

R2

0.896 0.829 0.535 0.535 CH3(o) –CH(i) CH3(i) –CH(i) −0.07 0.47 0.00 −0.08 0.999 0.999 0.04 0.47 −0.12 −0.09 −0.07 0.47 CH2(o2) –CH(i) CH2(i) –CH(i) 0.10 0.03 −0.17 −0.09 0.974 0.793 0.03 0.00 0.06 0.03 0.18 0.60 k = CH2(i) ; l = CH(i) i = CH3(i) i = CH3(o) i = CH2(o1) 0.27 0.11 1.06 0.31 −0.13 −0.35 0.706 0.499 0.862

0.892

Rik (exp) (Fi −Fk Rik )(exp) R2 Rik (calc) (Fi −Fk Rik )(calc) Rik (calc)b Rik (exp) (Fi −Fk Rik )(exp) R2 Rik (calc) (Fi −Fk Rik )(calc) Rik (calc)b

α(exp) β(exp) R2

i = CH(o) −1.45 1.19 0.499

CH2(o1) 0.31 0.13

CH2(o2) 0.02 0.08

CH2(i) 0.03 0.02

CH(o) 0.08 0.71

CH(i) −1.40 2.50

0.991 0.894 CH2(o1) –CH(i) 0.26 −0.11 0.997 0.07 0.33 0.23 CH(o) –CH(i) 0.26 0.69 0.944 0.28 0.47 0.32 i = CH2(o2) −0.25 0.28 0.254

a The following numbering scheme is used: o = outer ring, i = inner ring, CH = methyl, CH = methylene (labels 3 2

1 and 2 correspond to the different diastereotopic protons) and CH = methine.

b Values for the ﬁrst isostructural series (except Sm).

5. Application of the model-free methods to axial trimetallic lanthanide complexes with sterically rigid ligands Axial symmetry in trimetallic lanthanide complexes requires the location of the metal ions along the molecular threefold or fourfold axes. Since the terminal coordination sites are different from the central coordination site for symmetry reasons, two different crystal-ﬁeld paterminal central rameters B02 and B02 must be considered. Equation (61) holds for the general case of three (n = 3) magnetically non-coupled lanthanide metal ions packed along the symmetry axis and eqs. (62)–(64) can be used for homotrimetallic axial complexes. To the best of our knowledge, only one partial study of the NMR data for a D3 -symmetrical axial trimetallic complex has been reported (Bocquet et al., 2002; Floquet et al., 2003; see sect. 5.1.2). The D3h -symmetrical complexes [R 3 (L16 –3H)2(OH2 )6 ]3+ do not ﬁt the requirements for axial symmetry since the metal ions are located on mirror planes and not on the threefold axis, but

454

C. PIGUET AND C.F.G.C. GERALDES

the authors have applied pseudo-axial symmetry for their mathematical treatment (Chapon et al., 2001; see sect. 5.1.1). 5.1. Complexes with threefold symmetry 5.1.1. [R 3 (L16 –3H)2(OH2 )6 ]3+ (L16 = 1,3,5-triamino-1,3,5-tridesoxy-cis-inositol) The ligand 1,3,5-triamino-1,3,5-trideoxy-cis-inositol (L16 ) reacts with R(III) in water to give quantitatively the D3h -symmetrical trinuclear sandwich-type complexes [R 3 (L16 – 3H)2 (OH2 )6 ]3+ (Hedinger et al., 1998; ﬁg. 62). Toth et al. (1998) have used the gadolinium complex [Gd3(L16 –3H)2(OH2 )6 ]3+ as a model for investigating polymetallic MRI contrast agents and the selective formation of heterometallic analogues with lower symmetries [R 2 R’(L16 –3H)2(OH2 )6 ]3+ (C2v point group) and [RR’R”(L16 –3H)2(OH2 )6 ]3+ (Cs point group) has been demonstrated by Chapon et al. (2002). As far as NMR studies are concerned, 2D-EXSY spectra show that the complexes exhibit fast intramolecular rotation of the ligand with respect to the lanthanide ions on the NMR time scale, which corresponds to the rotations of the cyclohexane backbones about the threefold axis in the homotrimetallic complexes [R 3 (L16–3H)2 (OH2 )6 ]3+ (Chapon et al., 2002). Only para two 1 H NMR signals are detected for protons H1 and H2, and plots of δij /Sz j vs Cj /Sz j para (eq. (74)) and δij /Cj vs Sz j /Cj (eq. (75)) for [R 3 (L16 –3H)2(OH2 )6 ]3+ (R = Pr–Yb except Pm and Gd) display linear correlations which have been assigned to isostructurality along the complete lanthanide series (Chapon et al., 2001; ﬁg. 63), para

δij

Sz j

=

Cj

Fim

+

m=1

para

δij

3

=

3

m=1

3

B02 Gm i

√ + 6B22 Him

m=1

B02 Gm i

√ + 6B22 Him +

3 m=1

Fim

Cj , Sz j

(74)

Sz j . Cj

(75)

Fig. 62. Schematic formation of the D3h -symmetrical complexes [R 3 (L16 –3H)2 (OH2 )6 ]3+ in water with numbering scheme. The representation of the complex corresponds to the crystal structure of [Gd3 (L16 – 3H)2 (H2 O)6 ]Cl3 ·3H2 O, but the water molecules (two per R(III)) have been omitted for clarity (Hedinger et al., 1998).

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

455

para

Fig. 63. Plot of δij /Sz j vs Cj /Sz j (eq. (74)) for H1 in [R 3 (L16 –3H)2 (OH2 )6 ]3+ (R = Pr–Yb, D2 O, 298 K, adapted from Chapon et al. (2001)).

Since in the crystal structure the metallic sites are not located on the threefold axis (but on √ mirror planes), the rhombic term 6B22 Hi in eqs. (46), (48), (49) cannot be neglected and para para eqs. (74), (75) hold. However, it is worth noting that the δij /Sz j vs δkj /Sz j plot for H1–H2 in [R 3 (L16–3H)2 (H2 O)6 ]3+ (R = Pr–Yb except Pm and Gd) indeed gives a straight line which strongly suggest that the rotation of the cyclohexane backbone provides ‘effective axial symmetry’ in solution (Chapon, 2001; Briggs et al., 1972). 5.1.2. [R 3 (L17 )3 ]9+ (L17 = 2,6-bis{{1-ethyl-2-[6-(N ,N ’-diethylcarbamoyl)-pyridin-2-yl] benzimidazol-5-methylene}-(2-ethyl-benzimidazol-5-yl)}pyridine Strict axial symmetry results from the alignment of the three lanthanide ions deﬁning the threefold axis in the self-assembled D3 -symmetrical triple-stranded helicates [R 3 (L17)3 ]9+ . Thermodynamic studies display the quantitative formation of the trimetallic helicates in acetonitrile at concentrations compatible with NMR measurements. Variable-temperature 1 H NMR spectra of [R 3 (L17 )3 ]9+ (R = La, Y, Lu, 233–343 K) show diastereotopic methylene protons, in line with the formation of the expected rigid D3 -symmetrical structure on the NMR time scale (Bocquet et al., 2002; ﬁg. 64). Paramagnetic spectra for R = Ce–Eu, Yb have been assigned with classical NOE and COSY techniques, but detailed assignments for R = Tb–Tm require more sophisticated relaxation measurements which have limited structural analyses to the paramagnetic light lanthanides (R = Ce–Tb, Floquet et al. (2003)). Since (i) no magnetic coupling occurs at room temperature between the R(III) ions lying at distances larger than 4 Å and (ii) the tridentate binding units are separated by methylene bridges in L17 which are poor electronic relays, the contact contributions δijc result from through-bond Fermi interactions with a single metallic center and eq. (61) reduces to eq. (76) for [R 3 (L17)3 ]9+ in which Si is deﬁned in eq. (77). Different crystal-ﬁeld parameters for central terminal the central RN9 (B02 ) and the two terminal RN6 O3 (B02 ) metallic sites are rem m 2 quired together with three geometrical factors Gi = (3 cos (θi ) − 1)/(rim )3 deﬁned in ﬁg. 65 (m = 1, 2, 3). Equations (78), (79) correspond to the linear forms of eq. (76) used for testing

456

C. PIGUET AND C.F.G.C. GERALDES

Fig. 64. Schematic formation of the D3 -symmetrical complexes [R 3 (L17 )3 ]9+ in acetonitrile. The representation of the complex corresponds to the crystal structure of [Eu3 (L17 )3 ](CF3 SO3 )9 (CH3 CN)9 (H2 O)2 (Bocquet et al., 2002).

isostructurality (Floquet et al., 2003), para

= Fi Sz j + Cj Si ,

central 1 terminal 2 Gi + G3i , Gi + B02 Si = B02

(76)

δij

para δij

Sz j

= Fi + Si

para

δij

Cj

= Si + Fi para

(77)

Cj , Sz j

(78)

Sz j . Cj

(79) para

Plots of δij /Sz j vs Cj /Sz j (eq. (78)) and δij /Cj vs Sz j /Cj (eq. (79)) are linear for all aromatic protons (H1–H11) and for the methyl groups (Me17–Me20) along the series R = Ce–Eu in agreement with the existence of an isostructural series (ﬁg. 66). A ﬁrst set of Fi and Si factors obtained with eq. (76) has been used for predicting the 1 H NMR spectra of [R 3 (L17)3 ]9+ for the strongly paramagnetic lanthanides (R = Tb–Yb). Comparison between predictions and experimental data is only satisfying for the ﬁrst member of the second series [Tb3 (L17)3 ]9+ , thus allowing a complete assignment for this complex and its consideration

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

457

Fig. 65. Axial coordinates considered in trimetallic axial lanthanide complexes (adapted from Floquet et al. (2003)). Table 27 central 1 terminal 2 Gi + B02 (Gi + G3i )) terms and agreeComputed values for contact (Fi ) and pseudo-contact Si = (B02 ment factors (AFi ) for aromatic and methyl protons in complexes [R 3 (L17 )3 ]9+ (R = Ce–Tb, CD3 CN, 298 K, Floquet et al. (2003)). See ﬁg. 64 for the atom-numbering scheme Fi Si AFi Fi Si AFi

H1 −0.18(3) −0.08(1) 0.23 H9 −0.28(5) −0.27(1) 0.18

H2 −0.42(6) −0.03(2) 0.12 H10 −0.07(4) −0.23(1) 0.04

H3 −0.10(1) 0.025(2) 0.07 H11 −0.16(3) −0.17(1) 0.04

H4 0.043(4) 0.095(1) 0.02 Me17 0.01(4) −0.06(1) 0.29

H5 0.45(7) 1.20(2) 0.04 Me18 −0.01(2) −0.158(4) 0.05

H6 0.6(1) 1.20(3) 0.05 Me19 −0.02(1) −0.025(4) 0.33

H7 0.031(3) 0.068(1) 0.02 Me20 0.11(2) 0.470(5) 0.01

H8 −0.26(3) 0.05(1) 0.05

for the calculations of the ﬁnal set of Fi and Si factors collected in table 27. For R = Dy–Yb, the experimental 1 H NMR spectra do not ﬁt those predicted with eq. (76), which indicate a change of Fi and Si near the middle of the lanthanide series. Detailed analyses using crystalﬁeld independent equations related to eq. (51), but extended to trimetallic complexes, are currently in progress to detect possible changes of crystal-ﬁeld parameters occurring near the middle of the series. For R = Ce–Tb, the Wilcott agreement factors (eq. (57)) are acceptable for all aromatic protons (0.02 < AFi < 0.23, table 27), but the large AFi values observed for Me17 and Me19 result from minor paramagnetic shifts associated with negligible spin delocalization (Fi ) and dipolar effects (Si ). The Fi values are negligible for protons separated from the

458

C. PIGUET AND C.F.G.C. GERALDES

(a)

(b)

para

para

Fig. 66. Plots of (a) δij /Sz j vs Cj /Sz j (eq. (78)) and (b) δij /Cj vs Sz j /Cj (eq. (79)) for H10 in [R 3 (L17 )3 ]9+ (R = Ce–Tb, CD3 CN, 298 K, adapted from Floquet et al. (2003)).

paramagnetic center by more than ﬁve bonds, thus justifying that the contact contribution can be limited to a single magnetic center in [R 3 (L17 )3 ]9+ . Interestingly, Fi for the central pyridine protons H1 and H2 are larger than those found for the related protons of the terminal pyridine groups H9–H11 which strongly suggests improved spin delocalization onto the bis(benzimidazole)pyridine units. The structural factor Si is difﬁcult to interpret because it combines two crystal-ﬁeld and three geometrical parameters. The maximum values found for H5 and H6 conﬁrm the tight helical wrapping of the strands which forces them to point inside the triple helix and close to the metal ions (i.e., (rin )−3 are large). The larger values of Si observed for H9–H11 compared with those obtained for the central pyridine (H1–H2) are responsible for the strong paramagnetic shift experienced by the terminal pyridine ring, but its eventual assignment to speciﬁc geometrical parameters requires the evaluation of the crystalﬁeld parameters. Taking the crystal structure of [Eu3 (L17)3 ]9+ as a structural model for the solution structure, the geometrical factors Gm i (m = 1, 2, 3) have been calculated and a multi1 linear least-squares ﬁt of Si versus Gi and G2i + G3i for the eleven aromatic protons H1–H11 central

terminal

= −48(3) and B02 = −70(3). The quality of the linear correlation is satisgives B02 fying leading to an agreement factor AFS = 0.06 between calculated and experimental Si factors which indicates that only minor structural changes occur between the solid-state and the solution structures in these rigid polymetallic helicates. We can now rationalize the origin of the larger values observed for SH9–H11 compared to SH1−H2 which results from a combination terminal central of (i) the larger crystal-ﬁeld effects associated with the terminal sites (|B02 | > |B02 |) and (ii) the larger compensation effect resulting from opposite paramagnetic contributions in the central metallic site (i.e., G1i and G2i + G3i display opposite signs for all pyridine protons, central

terminal

(G2i + G3i )| = 1.7–1.8 are smaller terminal central (G2i +G3i )/B02 G1i | = 5.8–6.9 for H9–H11). We conclude from for H1–H2 than |B02

but the absolute value of the ratios |B02

G1i /B02

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS

459

the analysis of NMR data that the triple-stranded helical structure is maintained in solution for R = La to Lu and that isostructurality characterizes the ﬁrst part of the lanthanide series (R = Ce–Tb). However, an abrupt change of the crystal-ﬁeld parameters near the middle of the lanthanide series prevents the analysis of strongly paramagnetic complexes (R = Dy–Yb) with the one-nucleus technique (eq. (76), Floquet et al. (2003)).

6. Conclusions This survey of the applications of the model-free methods to axial lanthanide complexes with semi-rigid multidentate chelates demonstrates that any behaviour may occur along the lanthanide series. Structural changes are usually observed for ﬂexible complexes in which dynamic motions produce signiﬁcant distortions whose magnitude is controlled by the strength of the R–ligand interactions ([R(L3)3 ]3+ , [R(L7 –2H)3 ]3− ). On the other hand, the considerable rigidity imposed by podand ([R(L4 )3 ]3+ ), non-covalent podand [RM(L5 )3 ]5/6+ or macrobicyclic ([R(L6 )3 ]3+ ) ligands ensures well-deﬁned coordination sites and isostructurality along the complete lanthanide series. Surprisingly, the branched macrocyclic complexes [R(L10 –4H)]− , [R(L11 )]3+ and [R(L12 –8H)]5− are rigid enough to display different conformational isomers existing as non-interconverting species on the NMR time scale, but they adapt their cavity to the lanthanide contraction to such an extent that minor but signiﬁcant variations of the Fi and Rik parameters are systematically detected near the middle of the series. However, the most striking observations concern the rather systematic detection of concomitant changes in the crystal-ﬁeld parameter B02 and hyperﬁne constants (Ai ) near the middle of the lanthanide series for rigid, semi-rigid and ﬂexible complexes. At ﬁrst sight, such break could be traced back to the failure of Bleaney’s approach for modeling magnetic anisotropies. Although one cannot exclude that some speciﬁc ampliﬁcations of minor structural changes result from the larger Cj factors in the second part of the lanthanide series, the parallel variations of Bqk observed by eletronic spectroscopy in the solid state and the good correlations obtained between the Cj factors and the experimental anisotropic parts of the j susceptibility magnetic tensors (χzz − (1/3) Tr χ j ) for axial complexes, strongly support the view that Bleaney’s approach (i.e., a series limited to T −2 ) is a satisfying approximation. It remains that the multidentate ligands considered in this review often provide large crystalﬁeld splittings which probably do not satisfy the high-temperature hypothesis ECF /kT < 1. To the best of our knowledge, no attempt has been made to introduce the next T −3 term for the treatment of paramagnetic NMR data, despite the solid theoretical background proposed by McGarvey (1979). Further experimental justiﬁcations of the use of the limited hightemperature expansion for the magnetic susceptibility tensor is now required, but the recent successful applications of crystal-ﬁeld independent techniques (eqs. (51), (53), (68)) in axial complexes bring some support to the classical model-free approach (i.e., limited to T −2 ) because the removal of the crystal-ﬁeld parameter is only justiﬁed within Bleaney’s approach. We are convinced that further extensions toward rhombic systems and supramolecular polymetallic complexes are within reach and recent applications to bi- and trimetallic systems

460

C. PIGUET AND C.F.G.C. GERALDES

open fascinating perspectives for the design of lanthanide-containing paramagnetic probes with tuneable anisotropies.

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Mironov, V.S., Galyametdinov, Y.G., Ceulemans, A., Görller-Walrand, C., Binnemans, K., 2001. Chem. Phys. Let. 345, 132. Mironov, V.S., Galyametdinov, Y.G., Ceulemans, A., Görller-Walrand, C., Binnemans, K., 2002. J. Chem. Phys. 116, 4673. Morrison, C.A., Leavitt, R.P., 1982. In: Gschneidner, K.A., Eyring, L. (Eds.), Handbook on the Physics and Chemistry of Rare Earths, Vol. 5. Elsevier, Amsterdam, p. 461, ch. 46. Morrow, J.R., Amin, S., Lake, C.H., Churchill, M.R., 1993. Inorg. Chem. 32, 4566. Moussavi, M., De Cian, A., Fischer, J., Weiss, R., 1988. Inorg. Chem. 27, 1287. Ouali, N., Bocquet, B., Rigault, S., Morgantini, P.-Y., Weber, J., Piguet, C., 2002. Inorg. Chem. 41, 1436. Parker, D., 2000. Coord. Chem. Rev. 205, 109. Parker, D., Pulukkody, K., Smith, F.C., Batsanov, A., Howard, J.A.K., 1994. J. Chem. Soc., Dalton Trans., 689. Paulus, E.F., Juretschke, P., Lang, J., 1995. 3. Jahrestag der Deutschen Gesellschaft für Kristallographie, Darmstadt. Peters, J.A., 1986. J. Magn. Res. 68, 240. Peters, J.A., 1988. J. Chem. Soc., Dalton Trans., 961. Peters, J.A., Huskens, J., Raber, D.J., 1996. Prog. NMR Spectroscopy 28, 283. Petoud, S., Bünzli, J.-C.G., Renaud, F., Piguet, C., Schenk, K.J., Hopfgartner, G., 1997. Inorg. Chem. 36, 5750. Piguet, C., 1997. J. Chem. Educ. 74, 815. Piguet, C., Bünzli, J.-C.G., Bernardinelli, G., Williams, A.F., 1993. Inorg. Chem. 32, 4139. Piguet, C., Bünzli, J.-C.G., Bernardinelli, G., Hopfgartner, G., Petoud, S., Schaad, O., 1996. J. Am. Chem. Soc. 118, 6681. Piguet, C., Bernardinelli, G., Hopfgartner, G., 1997. Chem. Rev. 97, 2005. Piguet, C., Bünzli, J.-C.G., 1998. Chimia 52, 579. Piguet, C., Bünzli, J.-C.G., 1999. Chem. Soc. Rev. 28, 347. Piguet, C., Edder, C., Rigault, S., Bernardinelli, G., Bünzli, J.-C.G., Hopfgartner, G., 2000. J. Chem. Soc., Dalton Trans., 3999. Pinkerton, A.A., Earl, W.L., 1978. J. Chem. Soc., Dalton Trans., 267. Pinkerton, A.A., Schwarzenbach, D., 1981. J. Chem. Soc., Dalton Trans., 1470. Pinkerton, A.A., Rossier, M., Spiliadis, S., 1985. J. Magn. Reson. 64, 420.

PARAMAGNETIC NMR LANTHANIDE INDUCED SHIFTS Platas, C., Avecilla, F., de Blas, A., Geraldes, C.F.G.C., Rodriguez-Blas, T., Adams, H., Mahia, J., 1999. Inorg. Chem. 38, 3190. Platas-Iglesias, C., Piguet, C., André, N., Bünzli, J.-C.G., 2001. J. Chem. Soc., Dalton Trans., 3084. Pons, M., Millet, O., 2001. Prog. Nucl. Magn. Reson. Spec. 38, 267. Powell, D.H., Ni Dhubhghaill, O.M., Pubanz, D., Helm, L., Lebedev, Y.S., Schlaepfer, W., Merbach, A.E., 1996. J. Am. Chem. Soc. 118, 9333. Prins, L.J., Reinhoudt, D.N., Timmerman, P., 2001. Angew. Chem. Int. Ed. 40, 2382. Reilley, C.N., Good, B.W., Desreux, J.F., 1975. Anal. Chem. 47, 2110. Reilley, C.N., Good, B.W., Allendoerfer, R.D., 1976. Anal. Chem. 48, 1446. Ren, J., Sherry, A.D., 1996. J. Magn. Reson. B 111, 178. Ren, J., Springer, C.S., Sherry, A.D., 1997. Inorg. Chem. 36, 3493. Ren, J., Zhang, S., Sherry, A.D., Geraldes, C.F.G.C., 2002. Inorg. Chim. Acta 339, 273. Renaud, F., Piguet, C., Bernardinelli, G., Bünzli, J.-C.G., Hopfgartner, G., 1997. Chem. Eur. J. 3, 1646. Renaud, F., Piguet, C., Bernardinelli, G., Bünzli, J.-C.G., Hopfgartner, G., 1999. J. Am. Chem. Soc. 121, 9326. Reuben, J., 1982. J. Magn. Reson. 50, 233. Reuben, J., Elgavish, G.A., 1980. J. Magn. Res. 39, 421. Rigault, S., Piguet, C., 2000. J. Am. Chem. Soc. 122, 9304. Rigault, S., Piguet, C., Bernardinelli, G., Hopfgartner, G., 1998. Angew. Chem. Int. Ed. Engl. 37, 169. Rigault, S., Piguet, C., Bünzli, J.-C.G., 2000a. J. Chem. Soc., Dalton Trans., 2045. Rigault, S., Piguet, C., Bernardinelli, G., Hopfgartner, G., 2000b. J. Chem. Soc., Dalton Trans., 4587. Ruloff, R., Muller, R.N., Pubanz, D., Merbach, A.E., 1998. Inorg. Chim. Acta 275–276 , 15. Shannon, R.D., 1976. Acta Crystallogr. A 32, 751. Sharp, R., 2001. Nucl. Magn. Res. 30, 477. Sharp, R., Lohr, L., Miller, J., 2001. Prog. Nucl. Magn. Reson. Spec. 38, 115. Sherry, A.D., Singh, M., Geraldes, C.F.G.C., 1986. J. Magn. Reson. 66, 511. Sherry, A.D., Geraldes, C.F.G.C., 1989. In: Bünzli, J.C.G., Choppin, G. (Eds.), Lanthanide Probes in Life, Chemical and Earth Sciences, Theory and Practice. Elsevier, Amsterdam, ch. 4.

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Sherry, A.D., Ren, J., Huskens, J., Brücher, E., Tóth, É., Geraldes, C.F.G.C., Castro, M.M.C.A., Cacheris, W.P., 1996. Inorg. Chem. 35, 4604. Solomon, I., 1955. Phys. Rev. 9, 559. Spiliadis, S., Pinkerton, A.A., 1982. J. Chem. Soc., Dalton Trans., 1815. Spiliadis, S., Pinkerton, A.A., 1983. Inorg. Chim. Acta 75, 125. Spiliadis, S., Pinkerton, A.A., Schwarzenbach, D., 1982. J. Chem. Soc., Dalton Trans., 1809. Spiliadis, S., Pinkerton, A.A., Schwarzenbach, D., 1983. Inorg. Chim. Acta 75, 115. Spirlet, M.-R., Rebizant, J., Desreux, J.F., Loncin, M.-F., 1984. Inorg. Chem. 23, 359. Steed, J.W., Atwood, J.L., 2000. Supramolecular Chemistry. Wiley, Chichester. Stout, E.W., Gutowsky, H.S., 1976. J. Magn. Reson. 24, 389. Swiegers, G.F., Malefetse, T.J., 2000. Chem. Rev. 100, 3483. Swiegers, G.F., Malefetse, T.J., 2001. J. Incl. Phen., Macrocycl. Chem. 40, 253. Toth, E., Helm, L., Merbach, A.E., Hedinger, R., Hegetschweiler, K., Janossy, A., 1998. Inorg. Chem. 37, 4104. Ulrich, G., Ziessel, R., Manet, I., Guardigli, M., Sabbatini, N., Fraternali, F., Wipff, G., 1997. Chem. Eur. J. 3, 1815. Vold, R.L., Waugh, J.S., Klein, M.P., Phelps, D.E., 1968. J. Chem. Phys. 43, 3831. Wasylishen, R.E., 1987. In: Dybowsky, C., Lichters, R.L. (Eds.), NMR Spectroscopy. Dekker, New York– Basle, p. 45. Wertz, J.E., Bolton, J.R., 1986. Electron Spin Resonance. Chapman and Hall, New York–London, chaps. 3–5. Wilcott, M.R., Lenkinski, R.E., Davis, R.E., 1972. J. Am. Chem. Soc. 94, 1742. Wong, C.P., Venteicher, R.F., Horrocks Jr., W.deW., 1974. J. Am. Chem. Soc. 96, 7149. Wong, C.P., Horrocks Jr., W.deW., 1975. Tetrahedron Lett., 2637. Zhang, S., Kovacs, Z., Burgess, S., Aime, S., Terreno, E., Sherry, A.D., 2001. Chem. Eur. J. 7, 288.

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Handbook on the Physics and Chemistry of Rare Earths Vol. 33 edited by K.A. Gschneidner, Jr., J.-C.G. Bünzli and V.K. Pecharsky © 2003 Elsevier Science B.V. All rights reserved

Chapter 216 LANTHANIDE AND ACTINIDE SOLUTION CHEMISTRY AS STUDIED BY TIME-RESOLVED EMISSION SPECTROSCOPY Isabelle BILLARD Institut de Recherches Subatomiques, Chimie Nucléaire, B.P. 28, 67037 Strasbourg cedex 2, France

Contents List of symbols 1. Introduction 2. Basic principles of Time-Resolved Emission Spectroscopy (TRES) 2.1. Physical basis 2.2. Experimental 2.3. Data analysis 3. Physico-chemical modiﬁcations of the solution: Inﬂuence on the spectroscopic parameters 3.1. Introduction 3.2. Changes of solvent: Experimental data 3.3. Addition of supporting electrolytes: Experimental data 3.4. Temperature changes: Experimental data 3.5. General comments on the experimental data 3.6. First interpretation: Solvent effects onto the ﬁrst hydration sphere 3.6.1. Initial model: Solvated Eu3+ (or other lanthanide ions) in various solvents 3.6.2. First extension: Lanthanide and curium complexes in solution 3.6.3. Second extension: Solutions with supporting electrolytes 3.6.4. Discussion: Determination of the hydration number by TRES 3.7. Second interpretation: Förster mechanism 3.7.1. General theoretical approach 3.7.2. Use of a simpliﬁed formalism 3.7.3. Explicit use of the Förster mechanism

466 466 467 467 469 470 471 471 471 473 474 475 475

475 477 479 480 483 483 483 484

3.7.4. Discussion on the use of a Förster mechanism 3.8. Third interpretation: Empirical law for long range interactions 3.9. Conclusion on the question of hydration numbers and related topics 4. Reaction rate constants as studied by TRES 4.1. Theoretical approach 4.1.1. Stern–Volmer formula 4.1.2. Diffusion or activation-controlled reaction 4.1.3. Diffusion-controlled reaction: Smoluchowsky approach 4.1.4. Ionic strength effects 4.1.5. Electron transfer: Rehm–Weller equation 4.1.6. Time-dependent reaction rate constant and other modiﬁcations of the Stern–Volmer formula 4.2. Experimental data and links to theory 4.3. Conclusion on the study of reaction constants with TRES 5. Equilibrium constants and complexation as studied by TRES 5.1. Solvation/complexation: A brief introduction 5.2. Experimental data: Effects of complexation on the spectroscopic parameters 5.2.1. Absorption 5.2.2. Lifetime values and decay spectra 5.2.3. Excitation spectra and luminescence quantum yield 465

484 484 485 485 485 485 486 487 487 488

488 489 492 493 493 493 494 494 495

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5.2.4. Emission spectra 5.3. General considerations 5.3.1. Photophysical point of view and related experimental data 5.3.2. Chemical point of view and related experimental data 5.4. General kinetic scheme 5.5. Main results and physical implications 5.6. Discussion: Application to lanthanides and actinides

496 497 497 499 501 502 504

5.7. Conclusion on the determination of equilibrium constants by TRES 6. Analytical applications of TRES: A few examples 6.1. Trace amount determination of lanthanides and actinides 6.2. Trace amount determination of other ions 6.3. Luminescent lanthanide sensors 7. General conclusion References

506 506 506 508 508 509 510

List of symbols H O

D O

τobs , τobs2 , τobs2

experimental lifetimes of a lumines-

NH 2 O

hydration number

cent probe. When necessary, the sol-

kSV , kdiff , kact

Stern–Volmer reaction rate, diffusion contribution and activation contribution

vent is indicated as a superscript H2 O D2 O , kobs experimental decay rate of a lumineskobs , kobs

krad , knrad

cent probe. When necessary, the sol-

kB

Boltzmann constant

vent is indicated as a superscript decay rate of the radiative and non ra-

T η

temperature viscosity

diative process

ε

dielectric constant

Q, Q0 [M∗ ](t)

luminescence quantum yield concentration of the excited state M∗

K, Kapp kM , kML

equilibrium constants experimental lifetimes of species M

I, I0

at time t luminescence intensity

NEA

and ML Nuclear Energy Agency

1. Introduction Time-Resolved Emission Spectroscopy (TRES) is being increasingly used for the study of various chemical aspects of lanthanides and actinides in solution. These studies are related to deactivation mechanisms, luminescence enhancement, determination of equilibrium reaction rate constants, hydration numbers and analytical aspects such as the detection of trace amounts of species. In the case of actinides, the studies mainly deal with problems related to questions of nuclear fuel reprocessing and waste disposals. In this frame, some lanthanides, especially europium, are also studied as some of them are considered as good analogues of actinides. On the other hand, uranyl photophysics in solution has long been studied on more fundamental grounds. These include kinetic aspects of the Stern–Volmer type and non-radiative deactivation mechanisms. As a whole, lanthanide and actinide luminescence in solution as studied by TRES is of interest to a large community of scientists for both fundamental and applied aspects. This chapter deals with experimental TRES results and theoretical approaches that are relevant to the question of lanthanides and actinides solution chemistry. In this sense, this chapter

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does not intend to present a comprehensive bibliography but details publications that are of interest either from a theoretical or an experimental viewpoint. Publications dealing with solids will not be reviewed, except in few cases where such studies are of great interest for the general topics of this chapter. In principle, the luminescent species relevant to this work are: Lanthanides: Ce(III), Nd(III), Sm(III), Eu(II), Eu(III), Gd(III), Tb(III), Dy(III), Ho(III), Er(III), Yb(III). Actinides: U(VI), Np(VI), Am(III), Cm(III), Bk(III), Cf(III), Es(III). However, for many of these species, some peculiarities strongly limit the number of published data. From the actinide list above, Np(VI) luminescence has been observed and characterized only in solid matrix (Dewey and Hopkins, 2000). Bk, Cf and Es are hardly available in large quantities and few papers have appeared on Am(III), due to its very short luminescence lifetime, so that in practice, actinide luminescence studies are more or less restricted to U(VI) and Cm(III). Similarly, the extensive lanthanide list above is restricted mostly to Eu(III), Gd(III) and Tb(III), with fewer papers devoted to the other lanthanides. Note that Eu(II), although luminescent, is not stable in solution under “normal” conditions which limits the number of studies. As a consequence, this chapter reﬂects the tendencies described above by presenting examples mostly from Eu(III), Gd(III), Tb(III) and from U(VI) and Cm(III) studies. In solution, these ions are solvated so that either the subscript “aq” or “solv” will be used, depending on the solvent of interest. Finally, it is understood that the reader is aware of the basic principles of solution chemistry of lanthanides and actinides. Besides all the information published in the previous issues of this Handbook for lanthanides, excellent reviews exist on these topics, either on a general (Katz et al., 1986; Bünzli and Choppin, 1989; Grenthe, 1992; Choppin, 1997; Bünzli, 1998) or an historical perspective (Morss and Fuger, 1992).

2. Basic principles of Time-Resolved Emission Spectroscopy (TRES) 2.1. Physical basis For the general notions required, the reader is referred to a comprehensive publication (Birks, 1970). The brief presentation in this section aims only at setting basic principles. Once a species, M, has absorbed a photon of energy hν, an excited state is created, M∗ . Deactivation back to the ground state occurs through multiple steps, including very fast nonradiative processes that schematically correspond to energy transfers to the solvent. Radiative deactivation may also occur, leading to the emission of a photon of energy hν . Due to the nonradiative processes, hν < hν (Stokes shift). The emission spectrum is composed of bands, that are characteristics of the species. Besides the emission spectrum, the lifetime of the excited state is an important feature. Many organic ﬂuorescent molecules display “very short” lifetimes, in the pico- to nanosecond range, while the species of interest in this chapter (except Am(III) and Eu(II)) have rather “long” lifetimes, in the micro- to millisecond range. This lifetime value results from the combination of the two types of processes evoked above (radiative and non-radiative), together

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with the selection rules prevailing (e.g., “forbidden” transitions). This is described through eq. (1): −1 τobs = kobs = krad + knrad ,

(1)

where τobs is the lifetime of the excited state, kobs the global deactivation rate. The term krad in eq. (1) corresponds to an intrinsic phenomenon which is due to the electronic conﬁguration, while the term knrad stands for non-radiative deactivation processes, which depend on many factors, such as temperature, solvent etc. This aspect will be detailed in sect. 3. In the following, either τ or k values will be used. The ﬂuorescent quantum yield, Q, is deﬁned as: krad Q= (2a) . krad + knrad From eqs. (1), (2a) one easily derives the following equations that are of practical use: krad (1 − Q) , krad = Qkobs . (2b) Q In practice, it is very difﬁcult to measure an absolute ﬂuorescent quantum yield and experimentalists usually limit themselves to measure the relative ﬂuorescence yields. Turning to the basic kinetic aspects of the deactivation process, the equation describing the time-dependence of the excited species population, noted M∗ (t), is: knrad =

d[M∗ ](t) = −(krad + knrad )[M∗ ](t), dt from which one readily derives:

[M∗ ](t) = [M∗ ](0) exp −(krad + knrad )t ,

(3)

(4)

where [M∗ ](0) is the amount of excited state at time zero. The time dependence of [M∗ ](t) is a

decaying exponential and kobs = (krad + knrad ) is the decay rate of the excited state. However, the experimentalist has not directly access to [M∗ ](t) but only to the photons emitted by M∗ . The time dependence of the measured signal is therefore: dhν = krad [M∗ ](t). (5) dt This signal is also an exponential of rate kobs but the instantaneous amount of photons collected by the detector is related to krad , not to (krad + knrad ). The global ﬂuorescence intensity of M∗ , deﬁned as the integral of all photons emitted is equal to: ∞ krad dhν dt = [M∗ ](0) = Q[M∗ ](0). I= (6) dt (krad + knrad ) 0 The measured intensity is a function of the total number of excited species created by the excitation pulse and of the luminescence quantum yield, Q. In other words, for a given lifetime, the Q value determines the ease of detection of a given species. The notion of radiative vs. non radiative pathways is in fact very important as will be detailed below (sects. 3–5). In conclusion of this very brief description, the signature of an excited species in a given solution is composed of the emission spectrum and the lifetime value. This corresponds to 3D experimental data (intensity, wavelength, time) as is schematically depicted in ﬁg. 1. S(t) =

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Fig. 1. Schematic view of the 3D experimental data collected in Time-Resolved Emission Spectroscopy.

2.2. Experimental Most of the time-resolved emission spectroscopy setups are “home made” in the sense that they are built from individual devices (laser, detection system, . . . ) hence they are not of a “plug and press” type, so that their exact characteristics may vary from one installation to the other. Some of these differences have no impact on the overall capabilities of the system but some have a drastic inﬂuence on the way the collected data are processed and analysed. This aspect will be detailed in the next section, while this section deals with a general description of the apparatus. The most basic type of apparatus will be described, with no reference to sophisticated techniques such as Time Correlated Single Photon Counting or Circularly Polarized Luminescence devices. The excitation is performed by use of a pulsed laser delivering an appropriate wavelength. Due to the intense beam delivered, care should be taken to avoid multiple photon absorption and ﬁlter effects, due to a too large absorption of light. For lanthanide ions, as their absorption spectra are composed of rather narrow bands, an exact match between the laser wavelength and the absorption band is requested, so that a dye (liquid) or OPO (solid) laser is needed (for a complete set of absorption spectra of the lanthanides, see Carnall (1979)). For lanthanide complexes the absorption spectra partially overlap with those of the free ions, so that usually the same excitation wavelength can be used to induce the ﬂuorescence of both species. Fine tuning across the excitation spectra is possible (Wu and Horrocks, 1996). In this sense, Cm(III) is very similar to Eu(III). The particular case of excitation through energy transfer (antenna effect) will be discussed in sect. 5. In the case of the uranyl ion, the absorption spectrum is rather broad, so the third (355 nm) or fourth (266 nm) harmonic of a Nd:YAG laser can be used. The emission at 337 nm from a N2 laser is also possible. For all these lasers, the duration of the pulse is of the order of a few nanoseconds, which is three or more orders of magnitude below the lifetime of the ﬂuorescent probe under study. Therefore, the excitation process can be considered as instantaneous. The liquid sample, in a quartz cuvette, is kept in a thermoregulated chamber. The luminescence is emitted isotropically and its intensity is small

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as compared to the laser excitation pulse. Therefore, detection should be performed at right angle with respect to the laser beam direction, in order to avoid detector saturation. Schematically, two main systems can be used to collect 3D ﬂuorescence data (time, wavelength, number of photons, see ﬁg. 1). In a ﬁrst type of system, light is directed into a monochromator connected to a photomultiplier tube and then to a fast oscilloscope (PM detection). The experimentalist thus collects luminescence decays at various wavelengths. This system is known to be very efﬁcient for luminescence decay acquisition but is very time-consuming for the acquisition of emission spectra. In the second type of system, light is directed to a diode array detector (or CCD camera) and a subsequent electronic detection device (diode detection). The experimentalist collects emission spectra at various delay times (time zero for the pulse entering in the sample). This system is very efﬁcient for emission data acquisition but, on the other hand, time-consuming for luminescence decay acquisitions. From this very schematic description, it appears that a system combining the two types of detections would be the optimum. Finally, it has to be noted that whatever the detection chain used, the overall efﬁciency of the system is rarely constant over the whole acquisition range. The wavelength-dependent efﬁciency is not always taken into account in the published data. This has a priori no effect on the lifetime values but renders difﬁcult any comparison of emission spectra from one laboratory to another. Certiﬁed data are increasingly needed and requested by institutions, customers and the public. In the future more attention should be paid to corrected spectra, controlled data etc, even in basic research. 2.3. Data analysis In principle, emission spectra are easy to characterize through the position of the maxima. In contrast, luminescence decay analysis is not straightforward. As will be detailed later in this chapter, luminescence decays may be either mono- or multi-exponential and the determination of their exact nature is of paramount importance (see sect. 5). In the case of diode detection systems, the “physical” signal, as provided by the sample, is modiﬁed by the detection chain. In particular, it is integrated over short time delays, so that the ability of computer programs to extract lifetime values from such data set depends on the choice of these time delays and on the way they cover the time range of interest. Other difﬁculties may arise from the chemical nature of the sample: In some cases, the luminescence decay should be multiexponential, because of the phenomena involved in the solution under study, but the decay seems monoexponential, because some of the luminescent species emit with a very low intensity, as compared to the others. Another possible intricate situation is when the lifetime values are close to one another. A complete description of the difﬁculties possibly encountered is out of the scope of this chapter and the reader is referred to a speciﬁc publication on this question (Sharman et al., 1999). Other methods for multiexponential decay analysis are summarized in Bare et al. (2002). Furthermore, a recent round-robin test performed on aqueous solutions of U(VI) evidenced that, at least for the programs tested, improvements are required when more than two components are observed, in decays or emission spectra (Billard et al., 2003a). In this context, mathematical methods such as chemometrics (Adams, 1995) or global analysis

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(Janssens et al., 1990) or mixed methods (Al-Souﬁ et al., 2001) appear to be very promising in the ﬁeld.

3. Physico-chemical modiﬁcations of the solution: Inﬂuence on the spectroscopic parameters 3.1. Introduction In this section, experimental data on the spectroscopic changes observed upon modiﬁcations of the medium surrounding the luminescent probe will be ﬁrst presented. These changes do not include inner-sphere complexation of the probe itself, a topic examined in detail in sect. 5. However, the term “luminescent probe” may refer to a complex, for which the lifetime changes induced by modiﬁcations of the surrounding medium are investigated. The various models and empirical approaches that have been used to interpret the data will then be presented and discussed. 3.2. Changes of solvent: Experimental data The lifetime values of the luminescent probe in various solvents (either as a solvated ion or in a complexed form) are taken from the literature. However, considering the numerous publications available on lanthanide organic complexes (mostly of Eu(III)) that have been studied in water and in D2 O or some other solvents, it is out of the scope of this work to cite them all. Only some studies, which lead to very general conclusions of interest for the discussions below, are presented. In some cases, experiments have been performed in mixtures of two solvents, in various proportions. When speciﬁed in the publications, the decays are said to be strictly monoexponential. For the aqueous or solvated Eu(III) ion, tremendous variations of the lifetime are observed by changing the solvent as well as by using a deuterated analog of a given solvent. Some lifetime values are displayed in table 1. Similarly, strong modiﬁcations of the Eu3+ solv lifetime are observed in mixtures such as H2 O/CH3 COCH3 , H2 O/acetonitrile, H2 O/dioxane (Tanaka et al., 1988), H2 O/D2 O (Haas and Stein, 1971b), H2 O/DMF, H2 O/DMSO (Lis and Choppin, 1991) as a function of the water content. In H2 O/ethanol mixtures, modiﬁcations of both the lifetime and the emission spectrum are observed when EuCl3 is used, while no modiﬁcations of the emission spectra are detected for Eu(ClO4 )3 (Lochhead et al., 1994). Such modiﬁcations of the lifetime when passing from water to another solvent are also observed for the other solvated lanthanide ions (Carnall, 1979; Bünzli and Choppin, 1989; Kimura et al., 2001b). Some recent results are displayed in table 2. In the case of R(III) complexes, a strong inﬂuence of deuteration or solvent changes are observed (Bryden and Reilley, 1982; De Sa et al., 1993; Klink et al., 2000; Schuurmans and Lagendijk, 2000). Actually, in the case of Eu(III) complexes, it happens that the lifetime in D2 O is always larger than the lifetime in H2 O.1 In some cases, modiﬁcations of the emission spectra are also observed. 1 In the paper by Balzani and Sabbatini (1986), table 3, the larger lifetime in H O as compared to D O is a typing 2 2

error.

472

I. BILLARD Table 1 Lifetime values of Eu3+ solv in various solvents

Solvent H2 O D2 O CH3 OH CH3 OD CD3 OD CH3 CN CD3 CN Dioxane Dimethylformamide (DMF) DMF-d7 (CH3 )2 SO (CD3 )2 SO CH3 COCH3

τ (μs) 110 3600 or 4100 267 or 230 1408 4100 191a or 775 or 210 1400 159 1567 or 1700 2300 1500 or 1700 2850 or 3200 182

Ref. a a or d a or c a c a or b or d b a a or c c b or c b or c a

a Presence of crystallised water.

References (a) Tanaka et al. (1988) (b) Haas and Stein (1971a)

(c) Kimura et al. (2001b) (d) Bünzli and Choppin (1989)

Experimental conditions (a) T = 25 ◦ C, hydrated EuCl3 salt in D2 O or H2 O, Eu(ClO4 )3 in CH3 CN and CD3 CN, [Eu3+ ] = 10−2 M; (b) room temperature, perchlorate salt, [Eu3+ ] from 0.01 to 0.05 M; (c) T = 25 ◦ C, perchlorate salt, [Eu3+ ] = 10−2 M; (d) room temperature, perchlorate salt, [Eu3+ ] < 0.1 M. Table 2 Experimental lifetimes (μs) of some lanthanide ions in various solvents (from Kimura et al. (2001b)). Experimental conditions: T = 25 ◦ C, perchlorate salt, [R(III)] = 10−2 M. Theoretical radiative lifetimes (τrad , in μs) from Carnall (1979) Nd Sm Tb Dy

H2 O 0.032 2.7 430 2.5

D2 O 0.17 64 4100 43

MeOH 0.054 4.6 890 3.6

MeOD-d4 0.40 93 5200 69

DMF 0.49 20 1900 14

DMF-d7 2.0 250 2000 170

Table 3 Lifetime of solvated Cm3+ in various solvents. From Kimura et al. (2001b) Solvent H2 O D2 O MeOH MeOD-d4 DMF DMF-d7 DMSO DMSO-d6

τ (μs) 60 1200 190 800 420 770 870 1100

DMSO 2.0 22 2800 12

DMSO-d6 12 610 3200 330

τrad 420 6260 9020 1850

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Fig. 2. Variations of kobs (μs−1 ) for Cm(III) as a function of Xs , the mole fraction of the solvent in water. (•) methanol/water. () DMF/water. () DMSO/water. Redrawn from Kimura et al. (2001b).

Fewer papers have appeared for U(VI). In the case of the solvated ion, the solvent effect onto the lifetime is not drastic, with a factor of roughly two between H2 O and D2 O (Allsopp et al., 1979). For uranyl complexes in various solvents, see Yayamura et al. (1994). For Cm(III) and Am(III), the bibliography is somewhat scarce (Beitz, 1991; Kimura and Choppin, 1994; Kimura et al., 2001b). In the case of Cm3+ solv , see table 3 for some recent values. −1 In general, the variations of kobs = τobs are not a linear function of the molar fraction of one of the solvents in the mixture, whatever the ion studied. Typical curves are displayed in ﬁg. 2 for curium, considered as a typical example, also representative of Eu(III). From the wealth of data measured so far, it appears that linear variations of kobs are obtained only in the case of H2 O/D2 O mixtures, whatever the luminescent ions. In particular, in the case of H2 O/DMF or H2 O/DMSO mixtures, a linearity is obtained for τobs , not for kobs , up to 5 mol% (Lis and Choppin, 1991). 3.3. Addition of supporting electrolytes: Experimental data In this section, lifetime values (and in few cases, data on emission spectra) are collected for a luminescent probe in a given solvent, to which variable amounts of supporting electrolytes have been added. To the best of our knowledge, such experiments have been performed only for aquo ions (never for complexes), in H2 O or D2 O, but in two cases. Although the term “supporting electrolyte” implies no chemical reactivity towards the probe, results involving chloride based electrolytes, for which a complexation process is sometimes evoked in the case of lanthanides, are also presented in this section. When discussed at all in the literature, decay spectra are said to be monoexponential. In the case of lanthanides, all authors agree that the addition of perchlorate salts (NaClO4 , LiClO4 or HClO4 ) leads to a lifetime decrease for Sm3+ , Eu3+ , Tb3+ or Dy3+ in H2 O (Breen and Horrocks, 1983; Lis and Choppin, 1992; Kimura and Kato, 1998; Nehlig et al., 2003). In D2 O, the Eu(III) lifetime in presence of perchlorate based electrolytes decreases from roughly 4 ms (0.01 M) to 2.7 ms (above 8 M) (Lis and Choppin, 1992). The situation is more controversial in the case of chloride salts. According to some authors, the Eu(III) lifetime slightly decreases in H2 O solutions by addition of NaCl, LiCl or HCl (Lis and Choppin, 1992; Nehlig et al., 2003; Arisaka et al., 2002), while other authors observed no variation for

474

I. BILLARD

Eu3+ and Tb3+ and a very slight increase for Sm3+ or Dy3+ (Tanaka and Yamashita, 1984; Kimura and Kato, 1998). An effect of the cation associated to the chloride ion has been observed, as lifetime increases for increasing amounts of CsCl (Nehlig et al., 2003) while it decreases with LiCl in H2 O solutions (Nehlig et al., 2003; Arisaka et al., 2002). Spectral modiﬁcations (excitation and emission) parallel these lifetime changes in the few publications where these spectroscopic parameters have been measured (Breen and Horrocks, 1983; Nehlig et al., 2003). Finally, we note two publications where the effects of chloride based electrolytes have been examined in a H2 O/CH3 OH mixture for Eu3+ (Arisaka et al., 2001, 2002). In the case of U(VI) in H2 O, drastic lifetime changes are observed in the case of perchlorate based electrolytes (NaClO4 , HClO4 and mixtures of both), that have been experimentally studied in detail (Bouby et al., 1999; Rustenholtz et al., 2001). For example, the UO2 2+ lifetime increases from ≈ 2 μs ([HClO4 ] = 10−2 M) to 90 μs ([HClO4 ] = 10 M). Similarly to the europium case, an effect of the electrolyte cation has been observed: HClO4 induces a lifetime increase, while NaClO4 leads to a lifetime decrease. Furthermore, the effect of a given amount of NaClO4 depends on the amount of HClO4 . In such experiments, no spectral shift is observed. To our knowledge, no such experiments are available for Am3+ or Cm3+ , apart from one study for the system Cm3+ aq /LiCl (Arisaka et al., 2002). Note however that chloride ions are known to form inner-sphere complexes with Cm3+ and Am3+ (Allen et al., 2000) so that chloride based salts cannot be considered as supporting electrolytes in this case. 3.4. Temperature changes: Experimental data Surprisingly, studies devoted to temperature effects (in the liquid range) as such are very limited. Interesting results were obtained on the temperature dependence of the lifetime of an Eu(III) amino-diphosphonate complex, in H2 O and D2 O (Holz et al., 1990b). In both solvents, the lifetime decreases as temperature increases and this was ascribed to an additional (photoinduced) deexcitation pathway due to some ligand energy levels. In the case of uranyl, most of the available studies have been performed using rather high concentrations of nitrate salts of U(VI) (e.g., 0.2 M in Allsopp et al. (1979)) for which temperature-dependent complexation occurs (Grenthe, 1992). In addition, NO3 − is liable to complex radiolysis reactions that are also temperature-dependent (Mack and Bolton, 1999) so that the results of such studies may be an intricate combination of various temperature effects on the solvated UO2 2+ ion. Only one recent study has been performed with U(VI) using perchlorate salts, in sufﬁciently acidic solution (by use of HClO4 ) so that no anion complexation occurs. Thus, the results appear strictly ascribable to temperature effects onto UO2 2+ (Eliet et al., 1995). The lifetime changes follow a typical Arrhenius plot in the range 288–333 K, with an activation energy of (43.5 ± 1.8) kJ mol−1 , independent of the total HClO4 concentration. A very interesting feature of the decays is their non-exponential behavior at 288 K. Unfortunately, such studies have not been further detailed and the overall conclusions are rather limited, especially with respect to the emission spectra.

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3.5. General comments on the experimental data From the wealth of data outlined in the above sections, it can be seen that the lifetime is very sensitive to many physico-chemical changes in the surrounding medium of the luminescent probe (that should not lead to inner-sphere complexation, treated apart, see sect. 5), while the emission spectra are more or less not affected. Considering the brief theoretical approach of sect. 2.1, such changes are most probably only ascribable to changes in the knrad term of eq. (1), which substantiates the absence of signiﬁcant changes in the emission spectra. It is therefore tempting to search for a relationship linking the observed decay rate, kobs , to one basic physico-chemical parameter that is varied in a given experimental series. If possible, in order to be “user-friendly”, such a relationship should be as simple as possible, i.e., linear. Unfortunately, such an approach, to our opinion, is most of the time hopeless and may be misleading in certain cases. The nature of the effects observed will hamper any establishment of such a relationship, as the problem is obviously multiparametric in nature. Actually, changing the solvent or adding supporting electrolytes leads to modiﬁcations of many (if not all) physico-chemical properties of the medium, such as viscosity, density, dielectric constant, refractive index, conductivity, ion mobility, etc. However, usually one focusses on only one of these properties, not on their simultaneous variations. A plot of kobs as a function of any of these parameters will most likely lead to smooth or even linear variations, that may have no physical meaning, however. None of these parameters can be considered as the only “good” parameter and the joint variation of any physico-chemical parameter and the luminescence data must be examined with great caution before concluding on the existence of any real physical correlation. We would like, however, to moderate the pessimistic view that has been developed above by noting that actually, one-to-one correlations are experimentally obtained and that a ﬁrst approach to the problem, by seeking for linear correlations, is a necessary step towards the comprehensive understanding of the multiparametric phenomena involved. In the following, interpretation of the experimental variations detailed in sects. 3.2 and 3.3 are presented and discussed. 3.6. First interpretation: Solvent effects onto the ﬁrst hydration sphere This interpretation has been ﬁrst proposed in the mid 1960s by three groups of authors and since that time has been modiﬁed and extended in several steps that will be presented in a chronological order. 3.6.1. Initial model: Solvated Eu3+ (or other lanthanide ions) in various solvents Depending on the group of authors, such an interpretation is strictly limited to the lifetime variations of solvated lanthanides (Sm3+ solv , Eu3+ solv , Tb3+ solv and Dy3+ solv ) in D2 O/H2 O mixtures (Heller, 1966) or in other mixed solvents (Haas and Stein, 1971a, 1971b). For the latter, in addition to studies of ions such as Eu3+ solv and Gd3+ solv (Kropp and Windsor, 1965), attempts have been made to also include the case of europium complexes with sulfate or acetate (Kropp and Windsor, 1967) and this will be quoted in sect. 3.6.2. Two groups developed very similar reasonings (Kropp and Windsor, 1965; Haas and Stein, 1971a, 1971b).

476

I. BILLARD

In D2 O/H2 O mixtures (Heller, 1966), the kobs variations are ascribed to changes in the deactivation processes induced by OH and OD vibrations, which in turn leads to a decomposition of the expression of knrad (see eq. (2)) in a sum of terms: Q=

krad krad , = krad + knrad krad + kH [H]n + kD [D]m + ki [Qi ]

(7)

where kH and kD correspond to the contributions of H and D atoms to the overall value of knrad , respectively; [H]n and [D]m are the concentrations of these atoms with empirical powers and the last term takes into account the effect of other quenching species Qi , if present (e.g., impurities). Such an approach will be also used for the Stern–Volmer equation, see sect. 4.1.1. This equation is purely phenomenological, since it does not assume any particular quenching mechanism. Assuming that ki [Qi ] is negligible and denoting Q0 the ﬂuorescence quantum yield in a solution of D2 O, one obtains readily: kH Q0 =1+ [H]n . Q krad + kD [D]m

(8)

In this publication (Heller, 1966), the author measured the luminescence intensity ratio, denoted by I0 /I , which is proportional to Q0 /Q (cf. eq. (6) and sect. 2.1). For the experiments described, the I0 /I plot as a function of the H2 O concentration is linear in the very narrow range investigated (up to 8% of H2 O). On this basis, the author concluded that n = 1 and m = 0 in eq. (8). From the value n = 1, it is then deduced that “the radiationless relaxations studied involve only a single hydrogen atom”, which “leaves the OH bond as the only acceptable species”. Other species, like H2 O, HDO, H2 O·nD2 O and other aggregates are therefore not taken into consideration. The other group of publications corresponds to a two-step reasoning which is summarised as follows. In the ﬁrst step, the authors studied various pure solvents, such as H2 O, D2 O, CH3 CN, CH3 OH (Haas and Stein, 1971a; Kropp and Windsor, 1965). Using perchlorate salts of europium(III), the authors obtained the value knrad for various solvents by use of eq. (2b). From the values obtained, the authors divide the solvents into three groups, according to their quenching efﬁciencies, which are tentatively related to their chemical formula. In the second step, the authors restrict their study to the case of Eu(ClO4 )3 in CH3 CN, in which variable amounts of water are added (Haas and Stein, 1971b). The quantum yield of such solutions depends on the water concentration and is written as: Q=

krad . krad + knrad + kH [H2 O]

(9)

In this equation, it is assumed that the effect of the added water can be simply described through the term kH [H2 O], where kH is the bimolecular rate of deactivation of excited europium through OH bonds and [H2 O] is the water concentration. Again, Q and krad are experimentally measured so that: krad − krad = knrad + kH [H2 O]. Q

(10)

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477

2 Fig. 3. Variations of kobs (ms−1 ) for some Eu(III) solid compounds as a function of the number of water molecules in the ﬁrst coordination sphere (X-ray measurements). Solid line: linear regression for the data. Redrawn from Horrocks and Sudnick (1983).

H O

The experimental parameter [krad /Q] − krad is not a linear function of the water content in the whole range of concentration so that the authors restricted the ﬁt to the narrow range for which a linear plot is obtained, assuming that knrad is independent of the water content. The derived value2 is kH = 1100 M−1 s−1 (Haas and Stein, 1971b). This value is then related to the global quenching ability of water towards Eu(III), as determined in the ﬁrst step. Assuming that the deactivation mechanism quantiﬁed in the ﬁrst step can be only ascribed to the water molecules in the ﬁrst hydration sphere, the average hydration number of Eu(III) in pure water is thus equal to 9, which is in good agreement with the values obtained by other techniques. 3.6.2. First extension: Lanthanide and curium complexes in solution Since the 1980s, the concepts of the previous studies have been extended on the basis of a detailed experimental work (Horrocks and Sudnick, 1983). Note however that such an extension was clearly envisioned in a former paper (Kropp and Windsor, 1967). First, various solid state compounds of Eu(III) and Tb(III) have been synthesized with a known number of coordinated water molecules in the ﬁrst hydration sphere. X-ray diffraction experiments lead to the characterization of the structure of each compound. The decay rates H2 O of these solids, kobs , have been measured and plotted as a function of the number of water molecules in the ﬁrst hydration sphere (see ﬁg. 3). H2 O As can be seen from ﬁg. 3, the kobs values are a linear function of the number of water molecules, up to 9, to a good approximation. Thus, on the basis of the publications discussed in sect. 3.6.1, Horrocks and co-workers derive: H2 O kobs = krad + knrad + NH2 O kH2 O ,

(11)

where krad is the intrinsic decay rate and knrad represents all the deactivation pathways other than energy transfers through OH vibrations. The deactivation processes occurring through OH vibrations are described in the last term, where NH2 O is the number of water molecules in the ﬁrst coordination sphere, and kH2 O is the decay rate due to one water molecule. Assuming 2 In the cited publication, the unit (s−1 ) is erroneous and has been corrected in this text.

478

I. BILLARD

D2 O that the term (krad + knrad ) is equal to the decay rate of the luminescent probe in D2 O, kobs , this allows the determination of kH2 O for Eu(III) and Tb(III): H2 O D2 O (kobs − kobs ) , NH2 O

H2 O D2 O . − kobs NH2 O = α kobs

kH2 O =

(12a) (12b)

The conclusion drawn is that for solid compounds, eqs. (11), (12) apply and may be used for the determination of the number of water molecules in an unknown solid compound. The authors estimate the uncertainty to ±0.5 water molecule. Second, Horrocks and coworkers, and after them many others, have applied eq. (11) to Eu(III) or Tb(III) compounds in aqueous solutions, in order to determine the number of water molecules in the ﬁrst hydration sphere. The measurements were performed with TRES assuming that the decay rate is a function of the water molecules in the ﬁrst hydration sphere only. Similar studies leading to calibration laws of the type of eq. (12b) have been performed for Sm, Tb and Dy (Kimura and Kato, 1995, 1998) or Cm (Beitz, 1991; Kimura and Choppin, 1994). For Cm, the decay rate is measured in water/D2 O mixtures of known composition and for solid compounds doped with Cm. The crystallographic structures of these compounds have not been determined but assumed (Kimura and Choppin, 1994). Following this method, non-integer values of NH2 O are often found. Besides the uncertainty of the method, this is ascribed to the fact that NH2 O is an average of the dynamical equilibrium occurring in solution between water molecules of the ﬁrst hydration sphere and of the bulk. The method described above requires two measurements of the same compound: one in D2 O and one in H2 O. Therefore, in a third step, the method has been simpliﬁed by using a general calibration law for which only the experimental value in H2 O is needed: H2 O + B. NH2 O = Akobs

(13)

A and B are constants that can be determined for a given luminescent probe (i.e., Eu or Tb). Various values of A and B can be found in the literature and are presented in table 4. In this table, each expression is only referenced once, although it may have been used in numerous papers. More sophisticated expressions (see sect. 3.6.4) have not been included. Table 4 also displays the numerical values used in eq. (12b) (derived from Horrocks and Sudnick (1983)) for Eu(III) and Tb(III). The studies by Bryden and Reilley (1982), Wang and Horrocks (1997), Wang et al. (1999), already cited in the experimental section and others (Albin et al., 1984; Barthelemy and Choppin, 1989; Shin and Choppin, 1999), correspond to this approach, either in its “exact” (eq. (12b)) or “simpliﬁed” (eq. (13)) version. Finally, note that the authors using this method ascribe the decay rate changes mostly to the “water molecules” but that some authors use the more general term of “OH bonds”. This method has been further extended to non aqueous solvents, such as C6 H6 , where the number of H2 O molecules in the ﬁrst hydration sphere is deduced from the measurement of decay rates of some Eu complexes extracted in C6 H6 (Lis et al., 1991). In another paper, H2 O D2 O MeOH (k MeOD ) (Holz et (kobs ) by kobs eq. (12b) has been adapted to methanol, by replacing kobs obs

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Table 4 Numerical expression of eqs. (12b) and (13) used in the literature for various ions in water solutions (kobs expressed in ms−1 ) Ion Nd(III) Sm(III) Eu(III)

NH 2 O 3.58 kobs − 1.97 0.026 kobs − 1.6 0.0254 kobs − 0.37 1.1 kobs − 0.71 1.05 kobs − 0.44 1.07 kobs − 0.62 1.05 kobs − 0.70

Ref. a b a b a c d

2 −k 2 ) 1.05 (kobs obs 4.0 kobs − 1.0 4.03 kobs − 0.87

e b a

2 −k 2 ) 4.2 (kobs obs 0.024 kobs − 1.3 0.021 kobs − 0.6 2.56 × 10−4 kobs − 1.43 0.65 kobs − 0.88 0.612 kobs − 0.48

e b a a c a

H O

Tb(III)

H O

Am(III) Cm(III)

D O

D O

References (a) Kimura et al. (2001b) (b) Kimura and Kato (1995)

(c) Kimura et al. (1998) (d) Barthelemy and Choppin (1989)

(e) Horrocks and Sudnick (1983).

al., 1991) and the same method has been used in CHCl3 (Hasegawa et al., 1999). Numerical values obtained for H2 O/D2 O mixtures have been directly applied to H2 O/DMSO, H2 O/DMF, H2 O/MeOH and other mixtures (Kimura et al. 2001a, 2001b). It is interesting to note that the same type of interpretation (i.e., the role of OH oscillators in the knrad term) has been proposed for the Eu2+ lifetime changes induced by complexation with various cryptands and crown-ethers in methanol (for a review of this question, see Jiang et al., 1998). The experimental data are presented in sect. 5, which is devoted to spectroscopic changes induced by complexation. In the case of Eu2+ luminescence in solution, data are scarce because Eu(II) is easily oxidised into Eu(III). Thus, the quantitative interpretation of the data in terms of an equation such as eq. (12b) has not been performed. However, in view of the interesting discussion that has been initiated by Jiang and co-workers, these results will be discussed below in sect. 3.6.4. 3.6.3. Second extension: Solutions with supporting electrolytes Some authors attempted a description of the lifetimes changes induced by the addition of supporting electrolytes (sect. 3.3) by use of either the “exact” or “simpliﬁed” method proposed by Horrocks (Lis and Choppin, 1992; Kimura and Kato, 1998). By using eq. (12b) or eq. (13), one obtains an apparent increase in the calculated hydration number NH2 O as a function of the electrolyte concentration, which is surprising (from 9 to 11 in the case of Eu3+ in HClO4 /H2 O solutions, for example). In order to overcome this difﬁculty, it was suggested that the inner hydration number remains constant with an increasing quenching of the excited state as a

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I. BILLARD

function of the salt concentration. The increase would be due to stronger interactions of the Eu(III) ion with the OH oscillators already present in the inner coordination sphere (Lis and Choppin, 1992). This stronger metal-water interaction in the primary sphere would result from smaller interaction with water molecules in the outer hydration sphere caused by the increasing concentration of ions. 3.6.4. Discussion: Determination of the hydration number by TRES In the original papers, the important question of the possible hydrolysis of the solvated ion in the D2 O/H2 O mixtures is not addressed. It is assumed however that whatever the composition of the solvent, the aquo ion is, by far, the dominating species. From an experimental viewpoint, the initial D2 O concentration in the D2 O/H2 O mixture is controlled but the existence of HDO is not discussed. In one of these papers (Heller, 1966), the OH bond is considered as the only acceptable species responsible for the decay rate changes while H2 O, H2 O.nD2 O and aggregates are not considered at all; it is therefore somewhat difﬁcult to conceive the exact nature of these OH bonds. In two papers (Haas and Stein, 1971a, 1971b), the attribution of the non radiative effects to the water molecules in the ﬁrst hydration sphere is (strictly speaking) restricted to the case where the kobs variations are linear, which corresponds to a somewhat limited number of experiments, as was discussed in the experimental section. Finally, in the last paper (Kropp and Windsor, 1965), the deactivation process is clearly ascribed to OH and CH bonds. To conclude on this ﬁrst interpretation, it should be emphasised that these studies are the ﬁrst ones addressing a difﬁcult question, as the experimental section has shown. The physical bases included in eq. (7) appear reasonable, as it explicitly states that all the solvent molecules participate in the deactivation process. Furthermore, the assumption of speciﬁc deactivation efﬁciencies for all types of solvents is realistic. It should be noted that the absence of linearity of the kobs plots above a few water percents (except for the H2 O/D2 O mixtures) is a strong indication that all solvent molecules do not interact in an identical and independent way. Therefore, the extension made by Horrocks and collaborators (Horrocks and Sudnick, 1983) and by many other authors appears questionable. First, note that the interpretation of the lifetime values in solids is a rather difﬁcult task. Tremendous Eu(III) lifetimes changes in solids (from 1–2 ms to 50 μs, for example) have been ascribed to changes in the symmetry of the emitting center, a higher symmetry inducing a slower decay (Gaft et al., 2000a; 2000b, 2001). Second, all the studies based on eq. (13) rely on the assumption that the nonradiative deactivation process in solution is solely due to the water molecules in the ﬁrst D2 O hydration sphere, while by use of eq. (12b), which requires the measurement of kobs and H2 O kobs , the assumption is that the other non-radiative contributions are equal in H2 O and D2 O (and thus may not be negligible). The assumption embedded in eq. (13) is clearly an abusive extension of the results obtained by Haas and Stein (1971a, 1971b) and is in contradiction with the work of Kropp and Windsor (1965). This assumption totally neglects the role of other solvent molecules and anions as well as the non-linear variations of kobs in the case of non-aqueous mixtures. This last criticism applies to a limited number of papers but the general tendency with time evolves towards an extension of the so-called Horrocks’ method to various media such as non-aqueous liquid systems (Hasegawa et al., 1999; Holz et al., 1991;

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Lis et al., 1991), ion-exchange resins (Takahashi et al., 1997; Kimura et al., 1998; Arisaka et al., 2001, 2002) or hydrated zeolites (Suib et al., 1984) for which the direct use of eq. (12b) should be considered with caution. Actually, if H2 O were the only cause of deactivation, this would imply that the lifetime of a given R(III) ion in all solvents (except water) should be close to its radiative lifetime. Table 1 shows that the solvated Eu(III) lifetime is solvent dependent (radiative Eu3+ lifetime: 9.7 ms, from Carnall, 1979), tables 2 and 3 give a similar information for other R(III) solvated ions and Cm3+ solv , respectively. Examination of these tables shows that the contribution of D2 O molecules to the deactivation pathways cannot be neglected, as that of any other solvent. Turning to the case of R(III) complexes, it should be ﬁrst noted that the theoretical radiative lifetime of a given R(III) complex may be (very) different from that of the solvated ion (Werts et al., 2002). Therefore, the lifetime values of R(III) complexes in various solvents should be interpreted with caution. However, some experimental facts are in contradiction with eq. (13): (i) the deactivation efﬁciency of a ligand can be even lower than that of D2 O: in one case, an Eu(III) complex in D2 O has a lifetime (τobs = 4.66 ms) larger than that of Eu3+ aq in D2 O (Elhabiri et al., 1999); (ii) the lifetime of a Tb complex in D2 O is decreased by further complexation with various anions such as OH− , NO3 − , CH3 CO2 − , HCO3 − , citrate or CO3 2− (Dickins et al., 1998). In fact, the radiative lifetime value of a given complex is rather difﬁcult to derive and very few calculations (or data) are available so that comparison between krad and kobs values is only possible for Eu-dipicolinate complexes (Werts et al., 2002) (see table 5). Nevertheless, it can be seen that the ligand has an important impact onto the lifetime, even in D2 O (see table 5). In particular, it was shown in a very detailed study on Eu, Gd, Tb and Yb (Beeby et al., 1999), that the –OH, –NH and –CH bonds have an effect. A similar study has Table 5 Experimental lifetime values of various Eu(III) complexes in pure D2 O. Radiative lifetime values for some species Complex Eu3+ aq [Eu(dpa)]+ [Eu(dpa)2 ]− [Eu(dpa)3 ]2− [Eu(dota)]− [Eu(nota)] [EuL]− [EuL’]−

D O

τobs2 (μs) 3970 (a) 3560 (a) 3270 (a) 3320 (a) 2400 (b) 1700 (b) 2083 (c) 1850 (c)

dpa: dipicolinate; dota: 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetate; nota: 1,4,7-triazacyclononane-1,4,7-triacetate; L: 1,4,7,10-tetrakis(benzylphosphinate)-1,4,7,10-tetraazacyclododecane; L’: 1,4,7,10-tetrakis(methylphosphinate)-1,4,7,10-tetraazacyclododecane. References (a) An et al. (2000) (b) Supkowski and Horrocks (1999)

(c) Beeby et al. (1999) (d) Werts et al. (2002)

τrad (μs) theoretical/(experimental) 7700/(9500) (d) 4900/(6000) (d) 3100/(4300) (d)

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I. BILLARD

been limited to the –NH bond (Hnatejko et al., 2000). It was also shown that closely diffusing second-sphere solvent molecules have an inﬂuence onto the lifetime (Dickins et al., 1996; Beeby et al., 1999). A study considering all these effects can be found in Supkowski and Horrocks (1999). As a matter of fact, for a given ion, the large variations observed in the numerical values of B in eq. (13)—which is in units of (water) molecules—shed some doubts on the reliability of such a formulation (see table 4), unless a careful calibration is made and the equation used only for a given type of complex in a given solvent. In the case of solutions of supporting electrolytes, the use of the calibration relationship appears inadequate. The fact that the Eu3+ lifetime is changing by addition of NaClO4 in D2 O (see sect. 3.3) is by itself an indication that the H2 O molecules are not the only cause of the non-radiative deactivation process or, at least, that this is an indirect effect of the water molecules. As is quoted in sect. 3.6.3, in some cases, the calculated hydration number is increasing when the electrolyte concentration is increasing, which is difﬁcult to link to other experimental ﬁndings, although some doubts on that question have been raised (Kanno and Hiraishi, 1982; Kanno and Yokoyama, 1996). The qualitative explanation suggested an increasing quenching ability of each OH bond as a function of salt concentration is not in line with the physical concept of eq. (13) which is based on a quenching contribution of each OH oscillators independent of all others and limited to the ﬁrst hydration sphere. In the case of chloride based electrolytes, a detailed discussion on this point can be found in Nehlig et al. (2003). Recent experiments show that the structure of electrolyte solutions (in H2 O or D2 O) is very complex so that the notion of a single type of ﬁrst hydration sphere appears somewhat doubtful (Laenen and Thaller, 2001; Max and Chapados, 2002; Stangret and Gampe, 2002). Similarly, in the speciﬁc case of ethanol/H2O mixtures, it is well-known that hydrophobic aggregation takes place and is strongly dependent on the nature of the various introduced ions (Sacco and Holz, 1997; Sacco et al., 1998) so that the rather naive image of an homogeneous medium, which is actually embedded in eq. (13), has to be revised. Another fundamental questionable point can be raised by considering the temperaturedependent lifetime data of an Eu(III) complex (Holz et al., 1990b) (see section 3.4). One D2 O H2 O can take advantage of the kobs and kobs values that have been measured in the temperature range 278–363 K, in order to calculate the NH2 O variations as a function of T , by use of eq. (12b). While NH2 O is equal to 2.15 at T = 278 K, it raises as a function of T and reaches a value of 12 at T = 363 K. This latter value seems unphysically large. This most probably means that other deactivation pathways are available at high T . Conversely, it means that at any temperature, one has to discriminate between the contribution of such a phenomenon and of the envisioned OH oscillator effect, which appears a very difﬁcult task that has never been discussed, to our knowledge. In the case of the Eu(II) luminescence in methanol, the available data, that refer to the lifetime increase through complexation (see sect. 5) have been tentatively explained within the frame of OH bonds exclusion from the ﬁrst Eu(II) solvation shell. Interestingly, the values of τobs and τrad for various Eu(II) complexes in methanol were obtained. The discussion above has shown the great interest of such measurements which, in the case of Eu(II), are difﬁcult to perform due to the instability of divalent europium, and which should be more systematically performed in the case of trivalent europium. As compared to the solvated Eu2+ ion

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in methanol, the various complexes studied (mainly crown-ethers) display rather similar radiative decay rates and lower non-radiative deactivation rates. From these results, the authors concluded that water molecules in the ﬁrst solvation sphere are responsible for the deactivation pathways (Jiang et al., 1998). However, we do not agree with this conclusion: Similarly to the case of Eu3+ luminescence, comparison has to be made, for a given complex, between τobs and τrad values, whilst the comparison between the τobs values of the complex and of Eu2+ solv does not provide insight into this question, as explained above. The experimental data in methanol evidence a large effect of the type of ligand (for a given stoichiometry) onto the lifetime, as in the Eu(III) case. 3.7. Second interpretation: Förster mechanism 3.7.1. General theoretical approach The work of Förster deals with the problem of the energy transfer (non-radiative pathway) from a donor D∗ (created by absorption of a photon) to an acceptor A (see Förster (1959) for a good start in this theory, see Blasse (1990) for general aspects on the inﬂuence of ligands on luminescence and for a deeper look at the mathematics, see Voltz (1968)). Depending on the energy level matches between D∗ and A, such a transfer is more or less efﬁcient so that by modiﬁcations of the energy levels of A, either an inhibition or an enhancement of the ﬂuorescence of D∗ can be envisioned. The main physical parameters that are derived from the mathematical treatment are the energy transfer rate and R, the mean distance of interaction between D∗ and A. The transfer efﬁciency varies, in a ﬁrst approximation, as (1/R)6 . Other parameters of importance are the refractive index of the medium and the overlap between the emission spectrum of D∗ and the absorption spectrum of A. Although this theory is very general, Förster clearly stated that the following two cases can be described within this framework: (i) Energy transfer between independent species in solution (no chemical bond). (ii) Energy transfer between independent electronic systems of a given species. Therefore, the effect of a solvent onto the lifetime of a luminescent probe is ascribable to case (i) and the ligand effect to case (ii). In the ﬁrst case, experiments have shown that the typical interaction distance is of the order of 70 Å while it is 5 to 10 Å in the second case. The Förster theory is more accurate than the empirical formulation discussed in sect. 3.6.2. The following sections discuss the use that has been made of the Förster formalism. 3.7.2. Use of a simpliﬁed formalism Based on the experimental evidences discussed in sect. 3.6.4 of an effect of the ligand onto the lifetime, numerous publications have appeared that refer to the Förster’s theory (De Sa et al., 1993; Beeby et al., 1999; Supkowski and Horrocks, 1999; An et al., 2000). However, this theory is not applied in order to derive the transfer rate constant or the mean interaction distance value but only to justify the search for relationships between the observed decay rate and the number of OH, CH or NH bonds of the ligand, plus a global parameter for the solvent. Thus, although based on a very different theoretical approach, one deals with equations similar to eq. (11), with more terms, as in the following example (Beeby et al., 1999): kobs = krad + ksol + kCH + kNH + kOH + kC=O .

(14)

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I. BILLARD

3.7.3. Explicit use of the Förster mechanism In other studies, the aim is to determine whether the non-radiative deactivation mechanism is actually a Förster mechanism (other mechanisms, that have not been detailed in this paper, may lead to lifetime changes, especially at short interaction distances: Dexter mechanism or electron transfer, for example), and, if so, to derive the physical parameters relevant to this approach. For example, in the case of some heteronuclear lanthanide complexes, it was shown that the decrease of the donor quantum yield is not ascribable to a Förster mechanism (Tanaka and Ishibashi, 1996). In this very interesting study, both the ﬂuorescence decrease of the donor and the increase of the acceptor luminescence have been followed versus time. For other lanthanide complexes, a Förster mechanism has been assumed, in order to derive the mean interaction distance (Clarkson et al., 2000). Similarly, impressive results are obtained in the case of proteins (or other biological molecules) bound to lanthanides (Tb or Eu), where the distance between the absorbing chromophore and the luminescent metallic center has been measured (Horrocks and Sudnick, 1981). In one case, an unusual energy transfer (Förster’s theory) from a counter-ion towards Eu, Tb or Dy has been proposed, although the possible effect of the crown-ether cage was not fully ruled out (Tran and Zhang, 1990). Finally, although the mechanism is a Dexter transfer according to the authors, it is worth mentioning a study in xerogels doped with lanthanides (Buddhudu et al., 1999). Note that in the case where the Förster mechanism concerns an organic species transferring its energy to the lanthanide center to which it is bound, this is often referred to as the “antenna effect” and the ligand is sometimes called a sensitiser. Such an effect becomes efﬁcient provided that the organic chromophore possesses a triplet excited state close to but at least 1700 cm−1 above that of the lanthanide emissive state (Parker and Williams, 1996). 3.7.4. Discussion on the use of a Förster mechanism Although the theoretical approach appears to be valid, one may regret that some studies lead to equations that are not, in nature, very different from the empirical Horrocks’ method. In addition, as quoted by the authors of a very detailed work on this question (Beeby et al., 1999), the values of the kHX parameters in eq. (14) (X = O, C or N), were obtained for a speciﬁc donor-acceptor distance. They should be corrected for the (1/R)6 term for other ligands, which considerably lowers the general interest of eq. (14). In contrast, studies aiming at determining the exact nature of the non-radiative deactivation mechanism and the corresponding mean distance of interaction appear to be more in line with the Förster theory spirit and may be regarded as a fascinating attempt in this ﬁeld. However, applications appear rather limited as far as the question of the hydration sphere determination is concerned. 3.8. Third interpretation: Empirical law for long range interactions It may appear very tempting to apply the Förster’s formalism to the question of electrolyte effects onto the lifetime. However, some features of this effect render the use of the Förster’s theory difﬁcult: experiments with Eu have shown that the observed variations cannot be reproduced solely on the basis of the refractive index changes, a term included in the Förster’s

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expression (Schuurmans and Lagendijk, 2000). In addition, the non additive effect of anions and cations (see sect. 3.3, UO2 2+ case) is not included in the theory, which does not explicitly lead to an expression for the lifetime variations as a function of the electrolyte concentration. Therefore an empirical expression for the knrad variations has been proposed in the speciﬁc case of UO2 2+ in perchlorate based electrolyte solutions (Billard et al., 2001). It is based on the physical input of the Förster’s mechanism, i.e., on long-range interactions and energy transfers between the probe and the surrounding medium. The proposed expression contains a polynomial basis, which accounts for the increase in τobs as a function of [H+ ], together with additional polynomial, logarithmic and exponential terms involving [ClO4 − ] and [H+ ] in order to reproduce the effect of electrolytes composed of a mixture of HClO4 and NaClO4 (Billard et al., 2001). This empirical law was shown to be compatible with quenching experiments (see sect. 4 for a deﬁnition), thus demonstrating that this effect is actually due to knrad changes only. Similarly, empirical laws may also be found for the lanthanide case, although no study of this type has been performed yet. Considering the rather smooth kobs variations observed (Nehlig et al., 2003), it is most probable that second order polynomial expressions relating the concentration of the electrolyte ions to the kobs value would be sufﬁcient to reproduce the kobs variation observed in the lanthanide case. However, such empirical formulations have little interest as such: the important fact is that this electrolyte effect has been identiﬁed as being of physical instead of chemical nature. Obviously, such an approach is of no help for the determination of hydration sphere numbers and a comprehensive theoretical treatment of such effects is still needed. 3.9. Conclusion on the question of hydration numbers and related topics The spectroscopic characteristics of actinide and lanthanide luminescent probes are sensitive to numerous parameters, such as modiﬁcations of solvent composition, addition of supporting electrolytes, temperature changes etc. Therefore, TRES appears as an interesting tool for the chemist, because it provides sensitive experimental data. However, the interactions between the probe and the surrounding medium (in a wide sense) appear to be intricate and difﬁcult to handle. In this sense, attempts to describe lifetime variations as a function of a unique parameter, the hydration sphere number, have shown their limitations. On the other hand, the open questions related to Förster’s mechanism are a vivid and still not fully explored ﬁeld. 4. Reaction rate constants as studied by TRES In this section, the use of TRES for the study of a reaction rate constant will be discussed. In a ﬁrst step, the theoretical aspects will be presented and in a second step, the experimental data, mostly concerning U(VI), will be detailed. 4.1. Theoretical approach 4.1.1. Stern–Volmer formula The general frame is that of a reaction between an excited luminescent probe, M∗ , and another species, denoted by Q, following the scheme:

486

I. BILLARD

M∗ + Q

kSV

−1 kobs =τobs (hν )

hν

Z .

M It will be assumed that Q does not absorb the excitation light and does not react with the ground-state M. The decay rate of M∗ in the absence of Q will be denoted kM . Such a chemical scheme is independent of any effective mechanism for the interaction between M∗ and Q (Birks, 1970). It only states that, in the presence of Q, an additional deactivation pathway is present, through the creation of Z, which may be non-luminescent. By use of classical kinetic laws, one derives: d[M∗ ] (15) = −kM [M∗ ] − kSV [Q][M∗ ]. dt Supposing, which is correct most of the time, that Q is in large excess as compared to M∗ , and that kSV is time-independent, one obtains:

[M∗ ](t) = [M∗ ](0) exp − kM + kSV [Q] t . (16) Therefore, in the presence of Q, the observed decay rate of M∗ is equal to: kobs = kM + kSV [Q].

(17)

This is known as the Stern–Volmer equation, where kSV is the bimolecular reaction rate constant (in units of M−1 s−1 ). From an experimental viewpoint, the plot of kobs as a function of [Q] is a straight line, of slope kSV : the lifetime decreases as a function of [Q]. The global luminescence intensity of M∗ as a function of [Q] is equal to: ∞ ∞ kM kM dhν I= (18) dt = [M∗ ](0) = kM [M∗ ](t) dt = [M∗ ](0). dt kM + kSV [Q] kobs 0 0 This shows that the luminescence intensity decreases as a function of [Q] (Q is called a luminescence inhibitor or “quencher”), in parallel to the lifetime variation: no additional information is obtained by measurement of I as compared to lifetime measurements. In particular, the emission spectrum of M∗ is not distorted (no spectral shift) when Q is added to the solution. The exact chemical nature of Z cannot be deduced from the luminescence measurement of M∗ because the spectroscopic characteristics of Z do not appear in eqs. (15)–(18). Finally, it should be noted that, strictly speaking, the term “luminescence inhibition” and the Stern–Volmer equation should apply solely to experiments for which both the lifetime and the luminescence intensity decrease in parallel as a function of the concentration of a “quencher”. Finally, note that Stern–Volmer constants having a negative value have no physical meaning (Kessler, 1998). 4.1.2. Diffusion or activation-controlled reaction Solution reaction kinetics may be decomposed into two contributions. The ﬁrst one arises from the diffusion of the reactants and the second one corresponds to the chemical reaction itself.

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When the chemical reaction step occurs very rapidly (virtually instantaneously upon collision of the reactants), one speaks of a diffusion-controlled reaction and in this case, the reaction rate constant is typically on the order of 1010 M−1 s−1 . When the chemical reaction is slow as compared to the collisional process, the reaction is often called an activation-controlled reaction because a high activation energy is needed to yield the products. The rate constant is thus on the order on 1 M−1 s−1 . In the general case, the reaction rate constant is a combination of the two processes and is described by the following expression: 1

=

1

+

kSV kdiff where kdiff and kact

1 (19) , kact are the reaction rates of the diffusion and activation steps, respectively.

4.1.3. Diffusion-controlled reaction: Smoluchowsky approach A detailed presentation can be found in Steinfeld et al. (1999). In the case of neutral reactants, at inﬁnite dilution, the expression of kdiff is: kdiff =

2kB T (r1 + r2 )2 3ηr1 r2

(20)

where kB is the Boltzmann constant, T is the temperature, η stands for the viscosity and r1 and r2 are the ionic radii of the reactants. This equation is often called the Smoluchowsky relation but may present some slight differences from one author to the other, due to the various approximations made in the calculations. If the reactants are charged moieties, one has to consider the potential between them, which leads to another expression, sometimes referred to as the Debye expression: kdiff =

2kB T (r1 + r2 )2 3ηr1 r2

1 −z1 z2 e2 , 2 (r + r2 ) z1 z2 e 1 εkB T 1 − exp εkB T (r1 + r2 )

(21)

where ε is the dielectric constant of the solution and z1 , z2 the charges of the moieties. Some numerical applications allow to set limits for the kdiff values. For neutral species, the maximum value of kdiff (cf. eq. (20)) is on the order of 6 × 109 M−1 s−1 . For charged reactants, this value is increased by a factor 2 to 5 if the charges are of the same sign and is decreased by a factor of 0.2 for moieties of opposite sign. 4.1.4. Ionic strength effects If the two reactants are embedded in an electrolyte solution, the effects of the Coulomb attraction/repulsion terms are to be taken into account in the kSV expression. These correction terms are different in nature whether one considers the diffusion or activation contributions to kSV or not. For diffusion-controlled reactions the global effect of the electrolyte is to counterbalance the electrostatic effects between the reactants: the reaction rate will be increased for moieties of the same sign and will be decreased for moieties of opposite sign. The work of Debye and Hückel, based on the approximation that the solution is diluted enough to consider that

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I. BILLARD

Fig. 4. Schematic plot of log10 kSV as a function of the ionization potential (E0 , V ) of quenchers of similar chemical structures.

the electrolyte ions are not “too close” to each other, leads to the extended Debye–Hückel expression: √ log10 kSV = log10 k0 + 1.02z1z2 I , (22) where k0 is the kSV value as calculated in the absence of supporting electrolyte and I is the ionic strength of the solution. Considering the approximations made to obtain this expression, its limit of validity is roughly equal to 0.1 M. In the case of an activation-controlled process, the supporting electrolyte modiﬁes the activation coefﬁcients of the reactants and it is out of the scope of this work to enter in the mathematical treatment. A detailed approach of this case can be found in Simonin and Hendrawan (2001). 4.1.5. Electron transfer: Rehm–Weller equation In the above sections, nothing was said about the type of reaction between M∗ and Q. This is because the Stern–Volmer equation is model independent, as explained above and also because eqs. (20)–(22) are for a diffusion-controlled reaction. Some information can be obtained regarding an electron transfer from various quenchers of similar chemical structures towards M∗ . In this case, one may derive a relationship between kSV (as obtained from eq. (17)) and the ionization potential of these inhibitors. This is the Rehm–Weller equation, which is schematically depicted in ﬁg. 4. In this plot, the plateau value corresponds to kdiff . For a general overview of problems related to electron transfers, see Pouliquen and Wintgens (1988) (in French). 4.1.6. Time-dependent reaction rate constant and other modiﬁcations of the Stern–Volmer formula One of the basic hypotheses which sustains the Stern–Volmer equation is that the reaction rate constant, kSV , is time-independent. This is clearly an approximation. By assuming a timedependent kSV , integration of eq. (15) becomes tedious. Fortunately, this time-dependence is

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effective only at very short times as compared to the lanthanide and actinide excited state lifetimes, which allows one to neglect this dependence. However, this fundamental question (and also the spatial dependence of the reaction rate constant) is of great interest and is the subject of numerous theoretical and experimental works. In particular, Marcus’ theory shows that, for very negative ionization potentials, the plateau of the Rehm–Weller semi-empirical approach is no longer valid (inverted Marcus region) and that the electron transfer rate should display a bell shape as a function of the ionization potential. The reader will ﬁnd some recent advances on this questions in Scully et al. (1992), Tachiya and Murata (1992), Molski (1994), Berezhkovskii et al. (1998), Molski et al. (1998), Sikorski et al. (1998), Agmon and Gopich (1999). It is also possible that the properties of the solution induce some modiﬁcations of eq. (17). This is the case for example of a ﬂuorescent probe attached onto a polyelectrolyte: in this case, the high local concentration of ions strongly inﬂuences the rate constant so that eq. (17) is no longer valid. For one typical recent example of such a phenomenon with phenanthrene, see Morrison et al. (1996). 4.2. Experimental data and links to theory Numerous ions quench either the R(III) or U(VI) luminescence but most of the data available concern uranyl probes. Table 6 displays a selection of kSV values. Numerous additional kSV values for various alcohols/U(VI) systems can be found in the very comprehensive and interesting work of Cunningham and Srijaranai (1990), where kSV values vary from ∼ 106 M−1 s−1 to 1.5 × 109 M−1 s−1 in H2 O. Other values can also be found for an impressive list of quenchers of [UO2 F4 ]2− (Billing et al., 1991). A wealth of data can be found in Moriyasu et al. (1977b) for U(VI) in various complexing media such as H3 PO4 1 M. Among the somewhat unusual media in which such studies have been performed with U(VI), one can ﬁnd concentrated HNO3 aqueous solutions (Katsumura et al., 1989) and supercritical CO2 (Addleman and Wai, 1999). Note a very interesting study on enantioselective quenching for Eu(III), by use of the rather conﬁdential time-resolved chiroptical luminescence technique (Metcalf et al., 1990). Nothing on this topics is known for Cm3+ . Although experimental kSV values of some ions (NO2 − with Ce3+ or I− with UO2 2+ , for example) come close to the maximum value calculated from the Smoluchowsky equation (cf. eq. (21)), most of the inhibitors presented in table 6 do not correspond to diffusion-controlled reactions, as the kSV values are more than two orders of magnitude below the maximum (N3 − with Eu3+ or Dy3+ with UO2 2+ , for example). A solvent effect has been observed, with a kSV value in D2 O higher by a factor of two than that in H2 O for Eu3+ quenched by N3 − ions, but no explanation has been provided (Lis et al., 2001). No isotope or solvent effect has been found for alcohols and U(VI) (Cunningham and Srijaranai, 1990). Attention is drawn on the beautiful work about kSV values for various U(VI) complexes (Park et al., 1990) and also on a similar work, devoted to a more limited series of inhibitors (Lopez and Birch, 1997). Note that the smaller values obtained for uranyl complexes as compared to UO2 2+ aq are ascribable to a larger radius of this reactant, which limits its diffusion. Finally, some publications have presented kSV values for UO2 2+ using NO3 − or SO4 2− as U(VI) counter-ions. As these anions

490

I. BILLARD Table 6 kSV values (M−1 s−1 ) for various luminescence inhibitors. The solvent is H2 O, unless speciﬁed Inhibitor NO2 − N3 −

Experimentals [R3+ ] = 0.1 M; chloride salt; T = 25 ◦ C [R3+ ] = 10−2 M; perchlorate salt

kSV (M−1 s−1 ) 6.4 × 106 2.6 × 105 (H2 O) 5.3 × 105 (D2 O)

Ce3+ aq Dy3+ aq Sm3+ aq

NO2 −

[R3+ ] = 0.1 M;

chloride salt; T = 25 ◦ C

2.8 × 1010 4.7 × 108 3 × 108

a

Gd3+ aq

N3 −

[R3+ ] = 10−2 M; perchlorate salt

7 × 106

b

Tb3+ aq

N3 − NO2 −

[R3+ ] = 10−2 M; perchlorate salt [R3+ ] = 10−3 M; chloride salt

5.7 × 104 1.3 × 109

b a

Probe Eu3+ aq

Cl− Br− SCN− UO2 2+ aq

Dy3+ Gd3+ Eu3+

I = 3 M; pH = 3.4; T = 25 ◦ C; [UO2 2+ ] = 10−2 M; perchlorate salt perchloric medium [HClO4 ] = 1 M; T = 25 ◦ C; [UO2 2+ ] = 10−2 M [UO2 2+ ] = 4.6 × 10−2 M; perchloric media I = 3 M; [UO2 2+ ] = 5 × 10−3 M [HClO4 ] = 2.5 M; [UO2 2+ ] = 5 × 10−3 M [HClO4 ] = 0.4 M; I = 1 M; [UO2 2+ ] = 5 × 10−3 M

Cl− Br− I− SCN− Ag+

pH = 3.4; I = 3 M; T = 25 ◦ C; perchlorate salt; [UO2 2+ ] = 10−2 M [UO2 2+ ] = 4.6 × 10−2 M

I− Ag+

[(UO2 )2 (OH)2 ]2+

NO2 − I−

[UO2 F4 ]2−

UO2 (H2 PO4 )2

Br− Cl− SCN− N3 − Cl− Br− I− SCN− Cl− Br− I− SCN−

1.8 × 109 4.1 × 109 4.8 × 109 6.2 × 109 4.8 × 109 3.3 × 109 2 × 109 3.5 × 106 6.4 × 106 3 × 105 2.2 × 108 2.2 × 109 5.8 × 109 4.1 × 109 2.6 × 109

Ref. a b

c d e d f

c d

2.6 × 108 room temperature; [UO2 2+ ] = 10−2 M

I = 1.13 M; [UO2 2+ ] = 10−2 M

I = 2.2 M; [UO2 2+ ] = 10−2 M

1.5 × 109 1.5 × 109 3.5 × 106 1.4 × 109 3.5 × 108 1.8 × 107 8.9 × 108 3 × 109 1.9 × 109 4.5 × 107 8.5 × 108 2 × 109 1.6 × 109

g

c

continued on next page

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Table 6, continued from previous page Probe

UO2 SO4

Inhibitor Cl− Br− I− SCN−

Experimentals

I = 1.03 M; [UO2 2+ ] = 10−2 M

kSV (M−1 s−1 ) 3.8 × 108 2.5 × 109 4.6 × 109 3.8 × 109

Ref.

References (a) Tanaka et al. (1993) (b) Lis et al. (2001) (c) Park et al. (1990)

(d) Lopez and Birch (1997) (e) Moriyasu et al. (1977b) (f) Yamamura et al. (1999)

(g) Billing et al. (1991)

Fig. 5. Logaritmic plot of kSV as a function of (I )1/2 for various UO2 2+ inhibitors: (•) I− ; () Br− ; () Cl− . Redrawn from Yokoyama et al. (1976).

are well-known U(VI) complexing agents, caution should be paid on the exact attribution of the kSV constant to UO2 2+ aq or to a complex species (Burrows, 1990). In some publications about the ﬂuorescence of Eu(III) complexes, reference is made to the Stern–Volmer equation, although the authors clearly state that only the luminescence intensity decreases as a function of the “inhibitor”, while the lifetime remains constant (Parker et al., 1998; Parker, 2000). Ionic strength effects onto the kSV constant, as described by eq. (22), have been observed long ago, mainly for U(VI) (Yokoyama et al., 1976; Moriyasu et al., 1977b; Yamamura et al., 1999) but also for various lanthanides in the excellent work of Tanaka et al. (1993). Over the limited range of ionic strength investigated, it appears that eq. (22) is able to reproduce the experimental kSV variations, as illustrated in ﬁg. 5 for the UO2 2+ case. A recent work dealing with a wide range of ionic strength (10−2 to 9 M) shows that the kSV variations cannot be reproduced by this simple equation in this whole concentration range (Simonin et al., 2003). The ionic strength effect is not limited to kSV variation as described by eq. (22). The addition of large amounts of electrolytes may also modify the quencher solubility and thus its efﬁciency. This effect has been used by some authors, in systems very different from those examined in this work, in order to determine the association constant of the inhibitor salt (Mac, 1997; Mac and Tokarczyk, 1999): as the electrolyte concentration is increased, the quencher ion associates, so that the effective concentration of the inhibitor ion decreases, leading to a downward curvature of the Stern–Volmer plot. Such a curvature can be quantitatively related

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Fig. 6. Rehm–Weller plots for halogenide and pseudohalogenide inhibitors of some uranyl complexes. Redrawn from Park et al. (1990).

to the association constant of the inhibitor salt. This idea sustains the study of the inhibition of Eu(III) by NO2 − , which may be present in its associated HNO2 form (no quenching efﬁciency) or in its dissociated NO2 − form (maximum quenching efﬁciency) depending on pH (Tanaka et al., 1993). Numerous authors have shown that the Rehm–Weller equation is valid for the ﬂuorescence inhibition of various U(VI) species with alcenes (Park and Tomiyasu, 1992), heteroatomic (Park and Tomiyasu, 1993) or halogenated compounds (Burrows, 1990), as is illustrated in ﬁg. 6. This corresponds to the so-called normal Marcus region (which is thus also correctly described through the Rehm–Weller equation). This implies that an electron transfer occurs in such systems, from the inhibitor to the U(VI) species, leading to U(V), which disproportionates into U(IV) and U(VI). In one case at least, U(IV) has been observed, which strongly supports the proposed mechanism (Park et al., 1991; Park and Tomiyasu, 1992). Finally, lanthanides inhibit the UO2 2+ ﬂuorescence, most probably through an electron transfer (Yamamura et al., 1993, 1999). Apart from electron transfers at short distances that have been evidenced for some lanthanides (Tanaka et al., 1993), energy transfers through a Förster-type mechanism can also be responsible for the quenching (Tanaka et al., 1993). Finally, note an unusual paper where a theoretical approach related to the Marcus’ theory is applied to the reduction of lanthanide ions by hydrated electrons (Lee et al., 1998). 4.3. Conclusion on the study of reaction constants with TRES TRES is a valuable method to determine rate constants in the very speciﬁc case of a reaction between an excited species and a quencher. The theoretical approaches are easily applicable and lead to interesting results on various aspects of such reactions. Another type of reaction rate constant can be studied by TRES but is rather anecdotal: in the case where a ligand, L, reacts very slowly (on the order of hours to months) with the luminescent probe, the formation of the complex can be followed by TRES (for example, see Wu et al. (1996), Bazzicalupi et al. (2001)).

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5. Equilibrium constants and complexation as studied by TRES The measurement of equilibrium constants is a crucial aspect in lanthanide and actinide chemistry. Several techniques are available for such determination (spectrophotometry, potentiometry, solvent extraction, electrospray mass-spectrometry, . . . ), among which TRES is commonly used in the case of reaction studies of luminescent lanthanides with organic ligands (Richardson, 1982; Parker and Williams, 1996). The high sensitivity of TRES (see sect. 6) allows quantitative measurements of very dilute solutions, which facilitates the handling of highly radioactive materials such as Cm. In this section, the experimental changes in the luminescence characteristics of lanthanides and actinides upon complexation will ﬁrst be presented. Most of the work reviewed deals with aqueous solutions. The theoretical background will then be detailed and linked to the experiments. The consequences will be discussed in the last part of this section. 5.1. Solvation/complexation: A brief introduction As noted previously in this chapter, an ion in solution is not “free” but is solvated by solvent molecules. Usually, one refers to the ﬁrst solvation sphere but one may also deﬁne, for the sake of convenience, a second, a third etc solvation spheres, which are looser than the ﬁrst one. In fact, besides the ﬁrst solvation sphere, this notion is highly dependent on the technique used to determine it and the reader is referred to a review on this subject (Hinton and Amis, 1971). As explained before, in this chapter, we adopt the notation Xsolv for the solvated ion X. Strictly speaking, a solvated ion is complexed by the solvent molecules and this is particularly true for water as a solvent (Spencer et al., 1999). However, usually speaking, the term complexation only refers to the chemical acts that lead to an ion surrounded by at least one moieties different from the solvent, as long as a chemical interaction exists between them. Note that this new entity, which is called a complex, is also solvated but the subscript “solv” is usually omitted in this case (and is indeed omitted in this chapter). The notion of solvation and complexation are dynamic ones, as the ligand and the solvent molecules exchange with the bulk. Turning to the mechanism of complexation, two types of complexes can be envisioned: outer- and innersphere complexes. In the former case, the ligand and the central ion are separated by at least one solvent molecule. To form an inner-sphere complex, the entering ligand can expulse a solvent molecule (monodentate case) from the ﬁrst solvation sphere, so that the coordination number remains constant but a change in the coordination may also occur (reorganisation of the solvation sphere). Reviews exist on this subject for lanthanides (Bünzli and Milicic-Tang, 1995; Choppin, 1997; Bünzli, 1998) and for actinides (Nash and Sullivan, 1998). 5.2. Experimental data: Effects of complexation on the spectroscopic parameters For lanthanides, the wide question of the changes in the spectroscopic characteristics upon complexation has been already detailed in other publications (Bünzli and Choppin, 1989; Choppin and Peterman, 1998) but, to our knowledge, no similar work exists for actinides. Thus, in this chapter, the general trends will be presented for the various spectroscopic parameters with some emphasis on the actinide case, whenever possible.

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5.2.1. Absorption As was stressed above, in case of direct excitation of the lanthanides, the differences in the absorption spectra between the solvated ion and the complex formed are usually considered as slight but allow nevertheless the use of spectrophotometry for speciation purposes (for a recent example, see Giroux et al. (2000)). In the case of U(VI), the absorption changes observed upon complexation have often been used to determine equilibrium constants (for the classical example of U(VI) hydrolysed species, see Dai et al. (1998), Meinrath (1998)). For curium, no information of this kind is available: the low molar absorption coefﬁcient implies the use of solutions with high total curium concentrations, which are almost impossible to handle nowadays due to safety reasons. The absorption spectra of curium are known only for aqueous solutions of HClO4 (Carnall et al., 1958), HCl, H2 SO4 and HNO3 (Pascal, 1962). Another way of exciting the probe of interest in its complexed form is through the so-called “antenna-effect”, a notion relevant only for lanthanides and curium complexed to organic ligands. The basic principle is that of a Förster mechanism (see sect. 3.7.3): the ligand is excited with UV light and the energy is transferred to the metallic center, which then emits its speciﬁc luminescence. For very good publications on this aspect in the lanthanide case, the reader is referred to Parker and Williams (1996) and Bünzli (2003) and for an example in the case of curium, see Panak et al. (1995). Some applications of this phenomenon will be presented in sect. 6. 5.2.2. Lifetime values and decay spectra As can be deduced from sect. 2.1, complexation leads to lifetime changes. Again, due to the large number of studies devoted to very speciﬁc organic ligands of the lanthanides (for some examples, see Klink et al. (2000), Latva et al. (1997), Steemers et al. (1995), Wang and Horrocks (1997), Elhabiri et al. (1999) and others cited elsewhere in this chapter), it is out of the scope of this chapter to review them all. A short list of lifetime values for some Eu(III) complexes (in D2 O) has already been presented in table 5. The general trend is an increase of the lifetime through complexation. The range available is very large: for Eu(III) in H2 O solution for example, values from 119 μs (with terephtalate, 1:1 complex, Wang et al. (1999)) to 1 ms (with a macrocyclic ligand, Wang and Horrocks (1997)) or 3.9 ms (dipicolinate ligand, An et al. (2000)) can be found. Similarly, large variations in lifetime values can be found for a series of Eu(III) complexes extracted in C6 H6 (Lis et al., 1991). Eu2+ luminescence deserves a special mention (see sect. 3.6.4 for a discussion of the data presented here). While Eu2+ aq is known to be non-luminescent in water (Sabbatini et al., 1982), it emits weakly in methanol and the luminescence is greatly enhanced through complexation in this solvent (Jiang et al., 1998). In one case, a very weak emission has been observed in water for a Eu(II) complex (Sabbatini et al., 1984). As compared to the Eu3+ luminescence characteristics, Eu2+ always displays a rather short lifetime in methanol (in the range of 2 ns for solvated Eu2+ and up to 800 ns when complexed with 15C5).3 The detailed studies by Jiang and co-workers also provide data for the quantum yields, the radiative and non radiative contribution to τobs together with the emission spectra (Jiang et al., 1998). 3 Furthermore, the emission range is in the green part of the visible spectrum (roughly from 380 to 500 nm).

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For actinides, the general trend is also to an increase in the lifetime value upon complexation but the available range is more limited: for example, the 1:1 sulfato complex of U(VI) displays τobs = 4.3 μs (Geipel et al., 1996), UO2 F2aq is quoted with τobs = 250 μs (Beitz and Williams, 1997), while the ﬁrst two sulfato Cm3+ complexes present lifetimes equal to 88 μs and 95 μs (Fanghänel and Kim, 1998). However, this lifetime increase is not systematic and some carbonato U(VI) complexes have short lifetimes or exhibit no ﬂuorescence (Bernhard et al., 2001). In fact, a recent study on the application of TRES to U(VI) aqueous speciation has revealed that the lifetime of U(VI) complexes depends on the nature of the electrolytes added to the solution (Billard et al., 2003a). This effect is most probably similar to that discussed for solvated ions (see sect. 3.3) but has never, to our knowledge, been examined in details for lanthanide complexes. Nothing is known for Cm complexes on that question. In conclusion, the lifetime measured in solution is not an intrinsic (i.e., characteristic) parameter of a given species and precise indications should be given on the exact composition of the solution for the sake of comparison. The question of the decay behavior is not unimportant and will be discussed in the theoretical part in details (see also the discussion on data analysis in sect. 2.3). It is therefore of interest to review the experimental evidences on this point. For europium, depending on the ligand, the luminescence decays are either mono- or multi-exponential in the range of ligand concentration where both the solvated ion and the complex exist in solution (Ermolaev and Gruzdev, 1984; Horrocks and Sudnick, 1983; Wang et al., 1999). For all the (inorganic) ligands investigated with U(VI), the decay spectra are multiexponential, although two studies indicate a monoexponential behavior for U(VI)/F− (Beitz and Williams, 1997) and U(VI)/OH− (Meinrath et al., 2000). Note however that for these last two systems, such a monoexponential behavior was not conﬁrmed in a recent round-robin test (Billard et al., 2003a). For Cm3+ , it seems that inorganic ligands lead to a monoexponential behavior in solution (a bi-exponential behavior has been observed for Cm3+ embedded in a calcite lattice (Stumpf and Fanghänel, 2002)), while organic ones lead to a multiexponential behavior, whatever the ligand concentration is (Panak et al., 1995; Klenze, 2001). 5.2.3. Excitation spectra and luminescence quantum yield Due to the modiﬁcations of the electronic cloud induced by complexation, the quantum yield and the excitation spectrum are also modiﬁed. As the direct determination of the absolute quantum yield is very difﬁcult to achieve, one usually ﬁnds in the literature quantum yield values determined by comparison to well-known standards, such as quinine sulfate. For example, some values can be found in Georges (1993) or in Klink et al. (2000) for some europium complexes but may be found also in many other papers on lanthanide luminescence. Studies on the correlations between the photophysical properties of a given type of europium complexes and the energy levels can be found in Latva et al. (1997), Klink et al. (2000). A correlation has been found between the excitation properties and the stoichiometry of various Eu(III) complexes (Choppin and Wang, 1997). Note that the changes in the excitation maximum induced by complexation usually amount to a few tenths of nanometers, which requires high resolution for detection. In the case of Eu(III), a correlation has been found between the frequency

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of the 5 D0 ↔ 7 F0 transition and the nephelauxetic parameters of the coordinating atoms (Frey and Horrocks, 1995). Very little is known on these topics for actinides, as it seems that the determination of quantum yields is not a common feature in this case: To the best of our knowledge, a single publication gives a few values of luminescence quantum yields in various media for uranyl (Katsumura et al., 1989) and nothing is known for Cm. 5.2.4. Emission spectra In parallel to these lifetime changes, complexation induces tremendous modiﬁcations of the emission spectra, that have been examined for lanthanides in dedicated papers (for example, Hnatejko et al., 2000) or reviewed (Bünzli and Choppin, 1989). Brieﬂy, for Eu(III), taken as a typical example of R(III) ions, the emission arises from the 5 D0 → 7 FJ transitions, from which the 5 D0 → 7 F2 (around 616 nm) exhibits hypersensitivity. Therefore, the wealth of information experimentally obtained is highly dependent on the scanning step used and a high resolution is needed to make the best of an emission spectrum (Bünzli and Choppin, 1989). However, even in the case of a low resolution, the changes are spectacular, as illustrated in ﬁg. 7. When speciﬁc information on the symmetry of the complex is not sought (or needed), the ratio, R, of the intensity of the 5 D0 → 7 F2 transition to that of the 5 D0 → 7 F1 (around 592 nm) can be used as an indicator of complexation. For Eu3+ aq , this ratio is equal to 0.36 (Kim et al., 1994). The R value depends on the symmetry of the complex (Bünzli and Choppin, 1989), and values around 10 for complex with low symmetry are not rare (Lis et al., 1991). Conversely, low R value can be obtained, such as 0.67 for a centrosymmetric complex at room temperature (Klink et al., 2000) or 0.21 for a Th symmetry (T = 77 K) (Bünzli et al., 1999). For U(VI), complexation usually induces a red shift (typically of 3 to 5 nm) of the emission spectra. For Cm(III), complexation also induces red-shifts of a few nm of the whole spectra so that complexation is observed mainly as a shoulder of increasing importance as the ligand concentration is increased (Fanghänel and Kim, 1998).

Fig. 7. Emission spectrum of Eu3+ aq in slightly acidic aqueous (pH = 2) solution () and of its 1:1 complex with acetate (solid line). Units are arbitrary and the two spectra have been normalised at 592 nm.

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5.3. General considerations Obviously, TRES, by creating excited species, may be a very useful tool to study excited state chemistry (kinetics, equilibrium, etc.) but, as these excited species arise from the ground state ones, TRES may also give an insight into the ground-state speciation. In the case of lanthanides studied by TRES, it has always been considered that the reactivity of the excited-state simply mimic that of the ground-state (Horrocks and Sudnick, 1983; Ermolaev and Gruzdev, 1984). To our knowledge, a single group raised some doubts on this question (Marcantonatos et al., 1982) but the experimental evidences on which this hypothesis was proposed appear somehow thin. In contrast, diverging opinions are found for the uranyl case: photophysicists have long been interested in the UO2 2+∗ reactivity, which is considered to be very different from the reactivity of the UO2 2+ ground-state (Jørgensen and Reisfeld, 1982; Baird and Kemp, 1997). In the radiochemistry ﬁeld, however, it is mostly assumed that ground-state uranyl reactions only govern the speciation and that the various species formed, once excited, do not interact: the hypothesis of the UO2 2+ excitedstate reactivity has hardly been evoked in radiochemical studies (Beitz and Williams, 1997; Meinrath et al., 2000). Finally, for Cm3+ , although studies are relevant to the radiochemistry ﬁeld only, it is assumed that Cm excited-state reactivity exists and is similar to that of the ground-state. These opinions may appear rather contradictory at ﬁrst glance and it is the hope of the author to show in the following sections that they are in fact just two faces of a same problem. Therefore, before presenting the general theoretical treatment which allows to actually reconcile these various approaches, the experimental evidences on which these opinions are based will be shortly presented and their main basis summarized. 5.3.1. Photophysical point of view and related experimental data One of the main reasons of the interest in uranyl photophysics is that the photoexcited uranyl ion is one of the most oxidizing species known. Thus, two types of studies can be performed, either focussing on the photoreduction of U(VI) or on the oxidation of various moieties by U(VI)∗ . NMR (Rykov et al., 1991) or UV-Visible spectrophotometry can be used to follow the photoreduction/oxidation process. The species U(V) and/or U(IV) have been observed in various solutions such as H2 SO4 /H2 O/XeO3 (Khamidullina et al., 1994), lactic acid in water (Yokoyama et al., 1974) or in dry acetone (Sandhu et al., 1990). A special mention should be made on the ease of U(VI) photoreduction by alcohols (Bell and Billings, 1975; Katsumura et al., 1989; Cunningham and Srijaranai, 1990; Nagaishi et al., 2002) and on the complexity of the envisioned schemes (Arvis et al., 1983; Katsumura et al., 1989). Large effects of dissolved oxygen (Cunningham and Srijaranai, 1990; Rykov et al., 1991), of NO3 − (Katsumura et al., 1989) and of the irradiation time are found (Burrows et al., 1992; Khamidullina et al., 1994), which render the overall phenomenon difﬁcult to describe. Catalytic oxidation of cyclohexane has been observed (Mooney et al., 1988). Although very interesting, such studies are not perfectly in line with the general topic of this chapter and will not be discussed further. Pioneer studies have been performed in the late 1970s about various aspects of uranyl luminescence in solution, which appears to be sensitive to pH, temperature and to the addition

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of quenchers (in a wide sense). For a recent review on this subject (including solid state) see Baird and Kemp (1997). Below pH = 2, the decay spectra were claimed to present a biexponential behavior, correlated to signiﬁcant changes in the emission spectra. This was ascribed to the appearance of a new emitting center (Deschaux and Marcantonatos, 1979). The exact nature of this new emitting center was the subject of numerous publications, both on theoretical and experimental aspects (Marcantonatos, 1977, 1978, 1980; Marcantonatos and Pawlowska, 1989). Two models were put forward to describe the experiments: the group of Marcantonatos and co-workers suggested an exciplex, (U2 O4 H4+ )∗ , and the group of Burrows and co-workers proposed a distinct excited state, noted X∗ , linked to UO2 2+∗ by a reversible crossing mechanism (Miguel et al., 1984). The experiments on which this last hypothesis relied were made at higher pH value, typically from 3 to 4.5. A discussion was therefore started whether the observed changes at low and high pH values could possibly be due to the same phenomena. The theoretical aspects were rather detailed, including in some cases over 30 parameters in order to reproduce the entire set of data (Marcantonatos, 1980). Arguments in favor of either of the two models were proposed, based on the experimental emission spectra and oscillator strength theory, and electronic assignments were suggested. However, none of these publications paid enough attention to three problems related to the way the experiments were performed and which severely hamper the discussion on the possible existence of an exciplex or any other excited species: (i) most of these experiments were performed with high uranyl concentrations (0.1 M in Miguel et al. (1984) or 1 M in Azenha et al. (1991), for example) and the counter-ion was usually NO3 − , which is a well-known complexing agent of uranyl (Grenthe, 1992); (ii) the NO3 − ion is known to absorb the excitation wavelengths used, leading to the creation of radicals with a complex photophysics (Mack and Bolton, 1999); (iii) above pH = 3, the hydrolysis of the groundstate UO2 2+ ion is a well-known phenomenon, which has not been considered at all in the ﬁrst studies. All these problems shed doubts on the interpretations implying the formation of an exciplex or a reversible crossing mechanism, although the theory by itself is perfectly correct. In a very courageous paper, the group of Burrows admitted that its interpretation was misleading and that it is not necessary to consider an exciplex to interpret TRES data above pH 3, which were most probably ascribable to the excitation of hydrolysed groundstate species (Azenha et al., 1991). On the other hand, the experimental data of Marcantonatos and co-workers at low pH could not be reproduced by other groups (Park et al., 1990; Eliet et al., 1995) when NO3 − counter-ions were avoided so that the hypothesis of an exciplex formation (U2 O4 H4+ )∗ was abandoned in the early 1990s. Finally, on more general grounds, it is important to note that numerous photophysical studies are devoted to the determination of rate constants reactions between excited species (for two examples, see Laws and Brand (1979), Al-Souﬁ et al. (2001)). In such studies, it is taken for granted that if only ground-state chemistry is involved, simple relationships are to be found between the amplitudes of the emission spectra and the concentrations of the ground-state species and that the observed lifetimes represent the distinct decay rates of the non-interacting species. In contrast, in the case of excited state reactions, it is clear that neither of these simple relationships exist (Beechem et al., 1985).

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5.3.2. Chemical point of view and related experimental data From the experimental data brieﬂy described in sect. 5.1, one sees that TRES has considerable potential for the study of complexation reactions and thus for the determination of the equilibrium constant K. This objective has been the subject of a large number of publications so that only some of them will be reviewed here and the main aspects of this question, together with the so far unanswered questions, will be discussed. The determination of equilibrium constants from TRES experiments for lanthanide systems was ﬁrst described independently by Horrocks and Sudnick (1983) and Ermolaev and Gruzdev (1984). Based on the hypothesis of the similarity of the excited and ground state reactivity, it was said that TRES easily gives access to the equilibrium constant of the ground-state, K, for fast and slow photochemical processes; for intermediate rates of photochemical processes, it was said that no information on K can be derived. However, the original papers did not provide a clear experimental evidence of this statement. Nevertheless, the method has been extensively used for K-determination and some studies, by displaying excellent agreements between the equilibrium constants derived from TRES and by other means, have clearly shown the great interest of the method for lanthanide systems (see table 7 for some values). However, it has to be noted that the number of comparative studies of this kind for the lanthanide case is, actually, very limited, as comparison is often made with values for Sm or Gd (Gruzdev, 1983; Albin et al., 1984) or for chemical conditions that differ signiﬁcantly (Wu and Horrocks, 1997).

Table 7 Equilibrium constants, βx , as determined by TRES and other techniques for some Eu(III) and U(VI) systems. βx is deﬁned for the reaction: M + xL MLx (unless speciﬁed); βx = (MLx )/[(M)(L)x ] System M/L

Experimentals

K by TRES β1 = 105.25 β1 = 105.81

K by other means β1 = 105.08 β1 = 104.86

Eu3+ /hemimellitate Eu3+ /pyromellitate

TRES: pH 5.5 other: potentiometry, I = 0.1 M; T = 298 K

UO2 2+ /SO4 2−

TRES: (a) other: (b)

TRES: recalculated at I = 0 M other: recalculated at I = 0 M

β1 = 103.35 β2 = 104.21

β1 = 103.15 β2 = 104.14

TRES: (c) other: (e)

UO2 2+ /NO3 −

TRES: I from 0.3 to 6.4 M other: recalculated at I = 0 M

β1 = 10−0.47

β1 = 100.3

TRES: (d) other: (e)

UO2 2+ /HPO4 2−

TRES: T = 20 ◦ C; recalculated at I = 0 M other: potentiometry; T = 22 ◦ C; recalculated at I = 0 M

β1 = 1019.53 β2 = 1022.31

β1 = 1019.87 β2 = 1022.58

TRES: (f) other: (f)

a

a β is deﬁned for the reactions: x

UO2 2+ + PO4 3− + H+ UO2 (HPO4 ) UO2 2+ + PO4 3− + 2H+ UO2 (H2 PO4 )+

References (a) Wang et al. (1999) (b) Choppin et al. (1994)

(c) Geipel et al. (1996) (d) Couston et al. (1995)

(e) Grenthe (1992) (f) Brendler et al. (1996)

Ref.

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Table 8 Equilibrium constants, βx , as determined by TRES and other techniques for some Cm(III) systems. βx is deﬁned for the reaction: M + xL MLx ; βx = (MLx )/[(M)(L)x ] System M/L

Experimentals

K by TRES

K by other means β1 = 22 β2 = 73

Cm3+ /SO4 2− TRES: I = 2 M; T = 25 ◦ C β1 = 6.68a other: extraction, pH = 3; I = 2 M; T = 25 ◦ C β2 = 2.51

Ref. TRES: (a) other: (b)

Cm3+ /Cl−

TRES: I from 2.27 to 6 molal Other: ion exchange

0.02 < β1 < 0.046 β1 = 1.6 7 × 10−4 < β2 < 10−2 β2 = 0.9

Cm3+ /F−

TRES: T = 25 ◦ C; I = 0.5 molal Other: extraction; pH = 3.6, I = 0.5 M

β1 = 316b

β1 = 2.2 × 103 TRES: (c) other: (b)

Cm3+ /OH−

TRES: recalculated at I = 0 M; T = 25 ◦ C other: diluted medium; T = 25 ◦ C

β1 = 106.44

β1 = 106.3

TRES: (g) other: (b)

TRES: (a) other: (e)

a This system has been studied by TRES in the range of ionic strength from 10−2 to 6 molal, but β values are x

displayed only for I = 2 M, to allow comparison with other data from the literature.

b The β value at I = 0.5 M has been interpolated from the data provided in Ref. (c) to allow comparison with other 1

data from the literature. References (a) Fanghänel and Kim (1998) (b) Katz et al. (1986) (c) Aas et al. (1999)

(d) Wimmer et al. (1992) (e) Fuger (1992) (f) Grenthe (1992)

(g) Fanghänel et al. (1995)

In more recent years, the method has been directly applied to various systems containing curium: complexing anion such as F− (Aas et al., 1999), OH− (Wimmer et al., 1992; Fanghänel et al., 1994), 5-sulfo-salicylate (Klenze et al., 1998), CO3 2− (Fanghänel et al., 1998a, 1998b) and SO4 2− (Paviet et al., 1996) have been investigated. In these papers, reference to the theoretical result obtained on lanthanide systems is clear. Unfortunately, comparison between equilibrium constants as determined by TRES and other techniques is very difﬁcult for curium systems: in the past, solvent extraction or ion exchange were used (Katz et al., 1986) but these techniques require a large amount of radioactive material. Thus, TRES appears nowadays to be the only available technique, so that comparison with determinations performed using other techniques is only possible for a very limited number of systems. The comparison reveals some discrepancies, as illustrated in table 8. In the case of the Cm3+ /Cl− system, the rather large discrepancies are attributed to the fact that TRES is sensitive to innersphere complexes only, while other techniques do not make distinction between inner- and outer-sphere complexes, thus leading to an enhanced equilibrium constant, as compared to TRES (Fanghänel et al., 1995). However, this argument is not valid for sulfate complexation. In order to overcome the lack of stability constant data for Cm3+ , tentative comparisons have been made with known values for Pu or Am (Cm3+ /Cl− system, Fanghänel et al. (1995)) or with values for Tb, Sm, Am and Pu (Cm3+ /sulfosalicylate system, Klenze et al. (1998)). At the same time, uranyl reactivity has been studied by TRES without any reference to the theoretical results mentioned above for the lanthanides, as it was more or less clearly assumed that the uranyl excited-state reactivity is negligible (Geipel et al., 1996; Lopez and Birch,

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1997; Moulin et al., 1998; Rutsch et al., 1999; Eliet et al., 2000). As a matter of fact, the value of the equilibrium constant as determined by TRES for some uranyl systems are in very good agreement with the value obtained by other means (see table 7). A very limited number of papers on uranyl reactivity as followed by TRES suggested that the photoreactivity is not negligible (U(VI)/F− in Beitz and Williams, 1997 and U(VI)/OH− in Meinrath et al., 2000) but these results were not ﬁrmly assessed in a recent round-robin test (Billard et al., 2003a). 5.4. General kinetic scheme Considering the literature review above, it is necessary to develop a comprehensive view that may apply to any system, whatever the luminescent probe is, each system being considered as one speciﬁc case of a more general theory. In this section, we ﬁrst discuss the general scheme of (photo)chemical equations needed to describe a TRES experiment as well as a simpliﬁed scheme without photophysical reactions. The theoretical conditions to derive equilibrium constants from TRES data are discussed for the R(III), U(VI), and Cm(III) cases and are related to the experimental data presented above. A solution is supposed to contain two species, M and L, which form a 1:1 complex. The general reaction scheme after pulsed laser excitation of M can be described as in scheme 1. K is the equilibrium constant in the ground state, k1,2 are the reaction rate constants in the excited state and kM,ML are the intrinsic ﬂuorescence decay rates of M* and M*L, respectively. In this scheme, M is the ﬂuorescent probe and it is assumed that complexation, although modifying the electronic conﬁguration of M, still allows for luminescence to occur. In contrast, L is assumed not to absorb at the excitation wavelength. A typical TRES experiment consists in measuring time-resolved emission spectra as a function of the ligand concentration up to a large excess with respect to the concentration of the metal ion. Scheme 1 corresponds to the general situation where both ground-state and excited state reactions occur. One of the questions raised by Horrocks and Sudnick (1983) or Ermolaev and Gruzdev (1984) is under which conditions scheme 1, which leads to rather complicated rate equations, can be approximated by scheme 2, which neglects excited state reactions. In this model, Kapp stands for the apparent equilibrium constant. Whether or not Kapp is a good approximation for the constant K in scheme 1 is clearly an important question for experiments studying ground-state complexation reactions. As a whole, these two schemes and the conditions under which model 2 is a good approximation for model 1 (with the advantage M∗ + L

k2 k1

kM =1/τM

M+L

M∗ L kML =1/τML

K

ML

Scheme 1. Comprehensive photochemical kinetic scheme describing a TRES experiment.

M∗

M∗ L

kM =1/τM

M+L

kML =1/τML Kapp

ML

Scheme 2. Simpliﬁed kinetic scheme without photochemical processes.

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of an easier manipulation) correspond to the photophysical and chemical points of view discussed in sects. 5.3.1 and 5.3.2. The detailed mathematical treatment of these two schemes can be found elsewhere (Billard et al., 2003a) for time-independent reaction rate constants k1 and k2 and, for example, in Molski and Boens (1997), Molski et al. (1998) for time-dependent reaction rate constants. Note that the question of time and space-dependence of k1 and k2 , although very important and difﬁcult to solve (see sect. 4.1.6 for a insight onto this question), does not have to be considered here because such a phenomenon occurs on the pico- and subpicosecond time scale, which is far below the time resolution of usual TRES setups and the usual lifetimes of the luminescent probes of interest in this chapter. Therefore, this point will not be discussed further. It is out of the scope of this text to enter into the minute analysis of the mathematics and only the main results will be presented, focussing on the physical implications. 5.5. Main results and physical implications The time dependences of M∗ and M∗ L for schemes 1 and 2 are: Scheme 1: [M∗ ](t) = A exp(Λ1 t) + B exp(Λ2 t)

(23a)

∗

[M L](t) = C exp(Λ1 t) + D exp(Λ2 t) Scheme 2: [M∗ (t)] = [M∗ ](0) exp(−kM t)

(23b)

[M∗ L(t)] = [M∗ L](0) exp(−kML t) where Λ1 and Λ2 have negative values and are given by the roots of a second order polynomial, which depends on [L], kM , kML , k1 and k2 in a complex way: 1 Λ1,2 = − (kM + kML + k2 [L] + k1 ) 2 ± (kM + kML + k2 [L] + k1 )2 − 4[(kML + k1 )(kM + k2 [L]) − k1 k2 ].

(24)

For scheme 1, the luminescence decay, i.e. the time dependence of the sum of M∗ and reﬂects two decaying modes that are not speciﬁc to the two luminescing moieties M∗ and M∗ L: the two excited species both decay with two different lifetime values, (−1/Λ1 ) and (−1/Λ2 ), that are a function of [L] (eq. (24)).4 In contrast, in the case of model 2, each decaying species is characterized by its own lifetime, 1/kM or 1/kML , both independent of [L]. Conversely, one may consider the emission spectra and the intensities, Ji1 or Ji2 , associated with the emitting species M∗ and M∗ L under the frame of model 1 or 2: M∗ L,

Akrad,1 Bkrad,1 − Λ1 Λ2 Ck Dk rad,2 rad,2 J21 = − − Λ1 Λ2

Scheme 1: J11 = −

(25a)

4 As a consequence, attempt to use eq. (12b) to get an insight into the hydration number in this case is meaningless (Holz et al., 1990a).

LANTHANIDE AND ACTINIDE SOLUTION CHEMISTRY

krad,1 α[M] λ1 k β[ML] rad,2 J22 = λ2

Scheme 2: J12 =

503

(25b)

where α and β are deﬁned as follows: [M∗ ](0) = α[M], [M∗ L](0) = β[ML]. In both models, the two species M∗ and M∗ L have their own characteristic emission spectra, the intensities of which depend upon [L]. In other words, the total emission spectrum is the weighted sum of the individual contributions, which have very different expressions whether one considers model 1 or 2 (see eqs. (25a) and (25b)). Therefore, the emitting species M∗ and M∗ L can in principle be identiﬁed from a decomposition of the total emission spectrum, and thus TRES experiments are mainly based on the evaluation of emission spectra rather than luminescence decays. However, a detailed analysis of the decays allows one to derive important information that cannot be obtained through the emission spectra, as will be explained below. In the frame of model 2, it is easily shown that the expressions of the relative contributions of the two species to the global emission spectrum contain only one unknown parameter, Kapp , while the equivalent expressions under the frame of model 1 are much more complex. This raises the question as to whether model 2 can be considered a reasonable approximation of the more complex scheme 1. This issue can be discussed qualitatively on the basis of three distinct cases of model 1, depending on the importance of photochemical reactions. (i) If reactions in the excited state are negligible, i.e., if k1 and k2 are small as compared to the decay rates of the excited species (regime A), model 2 is obviously expected to be a good approximation of model 1. In this case, no signiﬁcant mixing occurs before the majority of excited species has decayed to their respective ground states. One obtains: Kapp = K.

(26)

This result is in agreement with those obtained by Horrocks and Sudnick (1983) and Ermolaev and Gruzdev (1984). Furthermore, under the frame of model 1 for slow excited state processes, the decays are multiexponential and the lifetimes do not vary signiﬁcantly with [L]. (ii) If the rate constants of the photochemical processes are on the same order of magnitude as those of the intrinsic decays (regime B), model 2 is not expected to be a good approximation for model 1. Again, this qualitative result is in agreement with the study of Horrocks and Sudnick (1983), even though the mathematical expressions presented in their work do not seem to be correct (Billard et al., 2003a). Under the frame of model 1, the decays are multiexponential but the photochemical processes induce a non negligible scrambling of the excited species, so that the lifetimes depend on [L], one decreasing and the other one increasing as [L] increases. (iii) The third case corresponds to rapid photochemical processes, where the equilibrium between the excited species is attained before a noticeable amount has decayed (regime C).

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In this case, it can be shown that one of the two lifetimes (−1/Λ1 ) or (−1/Λ2 ) vanishes, so that the luminescence decays appear monoexponential (model 1). Although this scenario differs considerably from the assumptions of model 2, one can nevertheless ﬁt the experimental emission spectra by use of model 2 in order to obtain an apparent equilibrium constant Kapp . The question remains as to the relationship between the derived Kapp value and the various parameters of the kinetic scheme 1. An expression of Kapp , based on a qualitative reasoning, can be obtained, by successively considering the three important steps of light absorption, equilibrium and decay to the ground state: the quantities of [M∗ ] and [M∗ L] generated by laser excitation depend upon the equilibrium constant K and the photoabsorption coefﬁcients α and β, a point already mentioned in Moriyasu et al. (1977a). The information on K which is contained in the values [M∗ ](0) and [M∗ L](0) is then lost due to the rapid photochemical processes deﬁned by the equilibrium constant in the excited state, K ∗ , which instantaneously leads to new values of [M∗ ] and [M∗ L]. Therefore, Kapp is proportional to K ∗ . For given values of K and K ∗ , an increase in α (all other parameters being unchanged) will create an increased amount of [M∗ ](0) which will be counterbalanced by an increased complexation through K ∗ . Conversely, an increase in β will induce an enhanced dissociation of M∗ L. Therefore, Kapp is proportional to the ratio (α/β). Finally, the time dependence of [M∗ ] and [M∗ L] is governed by two processes, the depletion by deactivation (kM and kML ) and the equilibrium reaction (K ∗ = k2 /k1 ). Assuming kM > kML , deactivation occurs predominantly via the channel M∗ → M. Thus, more photons come from the M∗ decay than expected if no dissociation of M∗ L would occur. With these considerations in mind, model 2 can be regarded as an approximation of scheme 1 with the following expression of Kapp : α τM Kapp = K ∗ (27) . β τML This qualitative result can be applied to any luminescent chemical system. It differs from the relation proposed in Horrocks and Sudnick (1983), which does not include the term (α/β)(τM /τML ). Finally, in the case of fast photochemical processes, the decays are monoexponential but the single lifetime is a function of [L] (see eq. (24)), and varies from τM ([L] = 0 M) to τML (L in large excess). In conclusion, the behavior of the luminescence decays allows one to determine to which regime (A, B or C) corresponds the system under study. For A and C regimes, the analysis of the emission spectra allows one to derive a value of Kapp , which can be easily related to K ∗ in the latter case and to K in the former. 5.6. Discussion: Application to lanthanides and actinides In the case of lanthanides, the 4f electrons, which are involved in the photoexcitation process, are strongly shielded. Hence one may assume that: K ∗ ≈ K.

(28)

This yields: Kapp ≈ K

α τM . β τML

(29)

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505

From the literature review proposed in sect. 5.2.3 regarding the decay behavior, the following conclusions can be drawn: (i) Uranyl systems correspond to regime A or B, with the possible exception of the F− ligand. (ii) Europium systems belonging to either one of the three regimes have been reported. (iii) Curium systems fall within regime C for all inorganic ligands investigated so far. Depending on the element of interest (R(III), U(VI) or Cm(III)), these results lead to different implications for the Kapp values as determined by TRES and how they can be related to K (eqs. (26)–(29)). For the uranium systems (except for F− , which is a doubtful case), the value of Kapp , determined by TRES and calculated according to model 2, is in fact equal to K (see eq. (26)). This is conﬁrmed in the case of the UO2 2+ /SO4 2− system (Geipel et al., 1996) by the very good agreement between the equilibrium constants as recommended by the Nuclear Energy Agency (NEA) and the value from TRES (table 7). In the case of europium complexation, depending on the type of ligand, TRES experiments give access directly to K (regime A) or cannot be used to derive K (regime B). For a system that falls within regime C, the determination of K is feasible, provided that the term (α/β)(τM /τML ) is measured or known: in fact, for the very few Eu(III) systems for which the Kapp value derived by TRES has been compared to the value derived by other techniques (see table 7), it happens that τML values are below 140 μs (Albin et al., 1984; Wang et al., 1999) while τM ≈ 110 μs (lifetime of Eu3+ aq ). This yields τM /τML ≈ 1–1.3. In addition, the strong shielding of the 4f electrons in lanthanide elements results in small variations of the absorption coefﬁcient upon complexation (Bryden and Reilley, 1982; Clarkson et al., 2000; Giroux et al., 2000), which would give α/β ≈ 1 for the excitation wavelengths used in these studies. Hence, the term (α/β)(τM /τML ) is expected to be close to unity. This explains the agreement obtained between equilibrium constants measured by TRES and other techniques (Wang et al., 1999). Finally, it is often noted in the literature, as a general remark, that the emission lifetimes in water for Eu (but also for Gd or Tb) are long enough, as compared to the ligand and water exchange rates, to consider that the lanthanide ion in its excited state reaches thermodynamic equilibrium with the ligand in solution. This remark is perfectly correct for regime C but is not applicable to regime A: as europium systems are found for which the luminescence decays are multiexponential, this means that k1 and k2 are small enough to avoid equilibrium between the excited species taking place within their lifetimes. Again, attention should be paid to the decay behavior in order to characterise the system. For the systems curium/inorganic ligands studied, on the other hand, the Kapp values derived by TRES are proportional to K ∗ rather than to K (see eq. (27)). To our knowledge, no simple relationship between K ∗ and K has been derived for 5f elements and the assumption K ∗ ≈ K simply relies on the similarities in the chemistry of 4f and 5f elements, a point which does not appear to be straightforward (Choppin, 1983). However, the question of a difference between K and K ∗ is not unimportant, as this difference can be very large in some systems, e.g., K ∗ = 10−2.8 and K = 10−9.5 for deprotonation of 2-naphtol (Laws and Brand, 1979).

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In addition, even under the assumption K ∗ ≈ K, the needed (α/β) value is difﬁcult to determine experimentally, because of the large amounts of Cm required for such a measurement. As a whole, although no precise information on possible differences between K ∗ and K can be given presently for Cm, it appears that the question of estimating the possible difference between these two quantities remains unanswered. This point is of a certain relevance for calculations of the migration of curium in the environment (Nitzsche et al., 2000). In this respect, some doubts have been shed on the K values determined by TRES for the two systems Cm3+ /CO3 2− and Cm3+ /SO4 2− by some authors (Felmy and Rai, 1999). 5.7. Conclusion on the determination of equilibrium constants by TRES TRES appears to be a sensitive tool to follow lanthanide and actinide complexation in solution, because most of the spectroscopic parameters are inﬂuenced by complexation. It has been shown that caution should be paid to the type of photochemical processes occurring in solution in order to correctly analyse the data. Taking account this important point, TRES is an interesting technique for the determination of equilibrium constants. From a more fundamental viewpoint, one may wonder why inorganic ligands lead to regime A with U(VI) and to regime C with Cm(III). However, the effective experimental problems encountered in the determination of Kvalues with TRES have not been discussed yet. These problems are of two distinct types. First, as already stressed, the correct analysis of a luminescence decay (i.e., mono- or multiexponential behaviour) is not a straightforward task, as has been shown in the case of welldeﬁned U(VI) systems (Billard et al., 2003a). In the case where more than two luminescent species are present in solution, overlap of the different emission spectra is also a problem, which limits the number of “ideal” systems to be studied. As a whole, it should be emphasized that TRES, although attractive, is not an “easy” technique and requires much effort, patience and great caution in data analysis. Second, nothing has been said in this section about the possible bias that can be generated by the photodegradation of the ligand, due to too intense irradiation. This point has to be avoided in TRES experiments but cannot be foreseen for a given ligand, especially organic or biological ones. A few publications of general interest are suggested on this point: Lao (1996), Holz et al. (1999), Nijegorodov and Mabbs (2000), together with publications directly related to this problem for lanthanide or actinide systems (Matsumoto and Azuma, 1988; Bouby et al., 1998; Morgenstern et al., 2000; Monsallier et al., 2001).

6. Analytical applications of TRES: A few examples 6.1. Trace amount determination of lanthanides and actinides When looking for R(III) determination, use can be made of the “antenna effect” already discussed in sect. 3.7, provided the lanthanide of interest is luminescent. The basic principle is to add a given organic ligand, which will ensure a high complexation constant with the lanthanide together with an efﬁcient UV absorption and energy transfer to the R(III)

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ion. The lanthanide luminescence can thus be detected down to the 10−10 M range, depending on the ligand and on the lanthanide. Note that the luminescence is so intense in most cases that time-resolved devices are usually not needed to achieve detection. A previous review has collected a large number of data on this question, to which the reader is referred (Horrocks and Albin, 1984); more recent papers on this topics present detection limits in the range 10−8 to 10−9 M, depending on the element (Berregi et al., 1999; Peter et al., 1992) and down to 0.11 ppt in the case of co-luminescence (Jenkins and Murray, 1996). Table 9 displays selected detection limits obtained for various lanthanides and actinides. Another possibility is to take advantage of the effect of various supporting electrolytes (in a wide sense) that act as luminescence enhancers, as discussed in sect. 3.3, such as phosphoric acid. This method has been investigated in details both for lanthanides and actinides Table 9 Detection limits for the determination of lanthanides and actinides as determined by TRES Element All RE (but Pm), La, Yb Mixtures of RE

Experimentals calcein complexation; 6.0 < pH < 9.2, depending on the element

Eu

DPA complexation; 7 < pH < 11 DPA plus columinescence (Yb) 3 M K2 CO3 medium

Limit of detection 5.2 × 10−8 M (Lu); 9 × 10−8 M (Ho); 6.9 × 10−7 M (La) 4.5 × 10−8 M (total concentration) 14 ppt 0.11 ppt 0.1 μg l−1

Tb

DPA complexation; 7 < pH < 11 DPA plus columinescence (Yb) DPA plus columinescence (Yb)

2.4 ppt 0.056 ppt 1 μg l−1

(c)

DPA complexation; 7 < pH < 11 3 M K2 CO3 medium

140 ppt 1.5 μg l−1

(b) (c)

DPA complexation; 7 < pH < 11 DPA plus columinescence (Yb) 3 M K2 CO3 medium

640 ppt 53 ppt 0.5 μg l−1

(b) (c)

concentrated H3 PO4

10 pptr 1 ng l−1

(d) (e)

TTA-TOPO/triton X-100 3 M K2 CO3 medium TTA-TOPO/triton X-100

≈ 10−8 M 5 × 10−11 M 4 × 10−13 M

(f) (g) (h)

Sm Dy U Am Cm

References (d) Kaminski et al. (1981) (e) Brina and Miller (1992) (f) Thouvenot et al. (1993)

(a)

(b) (c) (b)

DPA: 2,6-pyridinedicarboxylic acid; TTA: thenoyltriﬂuoroacetone; TOPO: tri-n-octylphosphine oxide. (a) Berregi et al. (1999) (b) Jenkins and Murray (1996) (c) Berthoud et al. (1989)

Ref.

(g) Decambox et al. (1989) (h) Moulin et al. (1991b)

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in various media of interest to the nuclear fuel cycle industry, such as solutions containing U and Pu (Berthoud et al., 1988; Moulin et al., 1996), human urines (Decambox et al., 1991) or blood (Scapolan et al., 1998) but also for natural waters (Moulin et al., 1990). The commercial complexing agent called “ﬂuran”, which is widely used for uranium detection, is a puriﬁed (uranium free) mixture of Na4 P2 O7 and NaH2 PO4 (buffer at pH = 7).5 For lanthanides, depending on the element, the detection limit is from 0.1 μg l−1 to 50 μg l−1 (Berthoud et al., 1989). For Cm, detections limits as low as 5 × 10−11 M (carbonated medium, Decambox et al., 1989) or 5 × 10−13 M (micellar system, Moulin et al., 1991b) were obtained. A summary of some detection limits can be found in Moulin et al. (1991a). In the speciﬁc case of the determination of trace amounts of actinides, it is interesting to compare the results obtained by TRES to those obtained by other techniques. This very brief presentation is based on a very detailed and comprehensive lecture on radioactive ultra-trace determination in the environment (Aupiais, 2001, in French). In order to detect radioactive traces in environmental samples, various techniques are available (α and β liquid scintillation, γ spectrometry, mass spectrometry, . . . ), which most of the time are coupled to a preconcentration of the sample. Such methods allow isotope discrimination, which is impossible with TRES. Another restriction of TRES as compared to the other techniques available is that TRES is strictly limited to luminescent elements. On the other hand, liquid scintillation is a rather time-consuming method as compared to TRES. For example, detection limits with α liquid scintillation are equal to 2 × 10−10 mol for 238 U and 9 × 10−19 mol for 244 Cm but the acquisition time is on the order of a few days, to be compared with TRES acquisition times of a few minutes. In the case of Cm, the advantage of α liquid scintillation is clear but TRES appears to be competitive in the case of U, if no isotopic discrimination is required. 6.2. Trace amount determination of other ions The Stern–Volmer equation (see sect. 4) may be used to determine small amounts of a species which would behave as an inhibitor of a given luminescent probe. The detection limit depends, among other parameters, on kM and on the detection limits of the setup. The potentials of this method for analytical purposes are discussed, on a general aspect, in Borissevitch (1999), Rakicioglu et al. (1998) and the speciﬁc cases of Eu(III) or U(VI) are presented in Georges (1993), Lopez and Birch (1996), Kessler (1998). For example, a detection limit of 7 ng l−1 for Cu2+ is obtained (Lopez and Birch, 1996). Numerous factors may render the method difﬁcult to apply: besides the variations of kSV as a function of ionic strength, if more than one quencher is present in solution, it becomes difﬁcult to determine their individual concentrations. This problem has been studied in the case of solutions that more or less mimic the nuclear fuel solutions in Katsumura et al. (1989). 6.3. Luminescent lanthanide sensors This subject is very important, vivid and passionating and has generated a wealth of speciﬁc publications and reviews. Although related to the main topics of this chapter, because of the 5 Mix equal volumes of solution A (Na P O C = 5 × 10−3 M) and solution B (NaH PO C = 0.4 M) before use. 4 2 7 2 4

If necessary, adjust to pH = 7.

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use of lanthanide luminescence, it is out of the scope of this chapter to make a comprehensive presentation of this subject. Therefore, we will restrict ourselves to a short presentation, making reference to a limited number of recent reviews on the subject to which the reader is referred to gain deeper information. For an historical perspective, see Soini and Lövgren (1987). The basic idea is to take advantage of the antenna effect (as described in sect. 3.7). The sensitiser, owing to its speciﬁc chemical structure, may be sensitive to changes in the solution (for example, protonation/deprotonation as a function of pH, presence/absence of a given moiety which will modify energy levels of the antenna through complexation). The energy transfer to the lanthanide will reﬂect these changes, and therefore the complex (antenna + lanthanide) will act as a sensor of some speciﬁc physico-chemical changes. This principle is very general and can be used with other metal ions than lanthanides. A recent review on this aspect for heavy and transition metal ions can be found in Rurack (2001). The physical principles detailed elsewhere in this chapter (Förster–Dexter mechanism, Stern– Volmer law, electron transfer, . . . ) directly apply to lanthanide sensors as detailed in two recent reviews on the subject (Parker, 2000; Bazin et al., 2001). Usually, the changes in the luminescence intensity is monitored but in the case of ﬂuoroimmunoassays, detection by use of time-resolved setups can also be of great interest (Hemmilä and Webb, 1997; Hemmilä and Mukkala, 2001). Note that detection through lifetime changes is also possible (Bare et al., 2002). In some cases, detection limits are very good (10−18 mol) (Hemmilä and Webb, 1997). In order to improve the sensitivity and the panel of sensors, the question then remains on how to design speciﬁc sensors. So far, lanthanide-based sensors have been successfully used for drug screening, assays and diagnostics as reviewed in Hemmilä and Webb (1997). Sensors for pH, pO2 and some anions (Cl− , CO3 2− , . . .) have been tested as exampliﬁed in Parker et al. (1998), Bazzicalupi et al. (2001). In the case where protonation/deprotonation of part of the ligand (in its excited state) is the sensor basis, the pKa of interest is that of the excited state, which may differ from that of the ground-state, as explained in sect. 5 (Parker et al., 1998; Blair et al., 2001).

7. General conclusion Through the various aspects treated here, the author hopes she has convinced the reader of the wide interest of TRES both for applied and fundamental aspects of lanthanide and actinide chemistry in solution. In particular, it was shown that theoretical approaches can be confronted to experimental data in ﬁelds as different as electron and energy transfers, ion interactions or photochemistry for example. In addition, TRES can be of great interest to the determination of equilibrium constants. Although nothing has been said in this chapter about micellar systems, colloids, solids and interfaces (in a wide sense), TRES is also a tool of large potential for the analysis of these media. TRES has been demonstrated to be of great interest for the study of U(VI) dissolved in supercritical CO2 (see, for example, the very good paper of Addleman and Wai, 1999). Other systems with high interest for TRES studies are Room Temperature Ionic

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Liquids (RTILs) and molten salts, two types of liquid media gaining increasing interest in various ﬁelds of chemistry: in addition to their general interest in “green chemistry” (RTILs) and in the nuclear fuel reprocessing industry (molten salts), their characteristics render them attractive for TRES experiments: they are transparent, photostable, and they can dissolve rather large amounts of various salts. Under such conditions, it is very probable that TRES will be used in the near future for the study of these liquids (Billard et al., 2003b).

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Suib, S.L., Zerger, R.P., Stucky, G.D., Morrison, T.I., Shenoy, G.K., 1984. J. Chem. Phys. 80, 2203. Supkowski, R.M., Horrocks, W.deW. Jr., 1999. Inorg. Chem. 38, 5616. Tachiya, M., Murata, S., 1992. J. Phys. Chem. 96, 8441. Takahashi, K., Kimura, T., Kato, Y., Minai, Y., Tominaga, T., 1997. Chem. Commun., 223. Tanaka, F., Ishibashi, T., 1996. J. Chem. Soc., Faraday Trans. 92, 1105. Tanaka, F., Yamashita, S., 1984. Inorg. Chem. 23, 2044. Tanaka, F., Kawasaki, Y., Yamashita, S., 1988. J. Chem. Soc., Faraday Trans. I, 1083. Tanaka, F., Ishibashi, T., Okamoto, M., 1993. J. Photochem. Photobiol. A 74, 15. Thouvenot, P., Hubert, S., Moulin, C., Decambox, P., Mauchien, P., 1993. Radiochim. Acta 61, 15. Tran, C.D., Zhang, W., 1990. Anal. Chem. 62, 835. Voltz, R., 1968. Radiat. Res. Rev. 1, 301. Wang, Y., Horrocks, W.deW. Jr., 1997. Inorg. Chim. Acta 263, 309. Wang, Z.M., van de Burgt, L.J., Choppin, G.R., 1999. Inorg. Chim. Acta 293, 167. Werts, M.H.V., Jukes, R.T.F., Verhoeven, J.W., 2002. Phys. Chem. Chem. Phys. 4, 1542. Wimmer, H., Klenze, R., Kim, J.I., 1992. Radiochim. Acta 56, 79. Wu, S., Horrocks, W.deW. Jr., 1996. Anal. Chem. 68, 394. Wu, S., Horrocks, W.deW. Jr., 1997. J. Chem. Soc., Dalton Trans., 1497. Wu, S.L., Franklin, S.J., Raymond, K.N., Horrocks, W.deW. Jr., 1996. Inorg. Chem. 35, 162. Yamamura, T., Park, Y.Y., Tomiyasu, H., 1993. J. Alloys Compounds 193, 186. Yayamura, T., Iwata, S., Iwamaru, S.I., Tomiyasu, H., 1994. J. Chem. Soc., Faraday Trans. 90, 3253. Yamamura, T., Fazekas, Z., Harada, M., Tomiyasu, H., 1999. Phys. Chem. Chem. Phys. 1, 3491. Yokoyama, Y., Moriyasu, M., Ikeda, S., 1974. J. Inorg. Nucl. Chem. 36, 385. Yokoyama, Y., Moriyasu, M., Ikeda, S., 1976. J. Inorg. Nucl. Chem. 38, 1329.

Handbook on the Physics and Chemistry of Rare Earths Vol. 33 edited by K.A. Gschneidner, Jr., J.-C.G. Bünzli and V.K. Pecharsky © 2003 Elsevier Science B.V. All rights reserved

Chapter 217 OPTICAL STUDIES OF NON-METALLIC COMPOUNDS UNDER PRESSURE Thomas TRÖSTER Universität Paderborn, FB 6 / Physik, 33095 Paderborn, Germany

Contents List of symbols and abbreviations Introduction High pressure technique Survey of experimental data Energy levels 4.1. Theoretical background 4.2. Line shifts 4.3. Nephelauxetic effect 4.4. Crystal-ﬁeld splittings 4.4.1. Crystal-ﬁeld parameters 4.4.2. Local distortions 4.4.3. Superposition model 4.4.4. Ab initio calculations 4.4.5. Correlation crystal ﬁelds 4.4.6. Excited states 4.5. Pressure sensors 4.6. Structural probes

1. 2. 3. 4.

515 516 517 520 520 520 527 529 535 535 540 541 545 547 548 552 555

4.6.1. Multiple sites/glasses 4.6.2. Phase transitions 5. Intensities and lifetimes of f-f transitions 5.1. General considerations 5.2. Absorption studies 5.3. Luminescence studies 5.3.1. Inﬂuence of 4fN−1 5d1 conﬁgurations 5.3.2. Inﬂuence of charge transfer states 5.3.3. Energy transfer processes in insulators 5.3.4. Energy transfer processes in semiconductors 6. Electron–phonon interaction 7. Conclusions Acknowledgement References

List of symbols and abbreviations k (R) B

intrinsic crystal-ﬁeld parameters

HOMO

Highest Occupied Molecular Orbital

Bqk

crystal-ﬁeld parameters

intensity total angular momentum

Cq

tensor operators

I J

CFCM CTS

central-ﬁeld covalency model charge transfer state

L LUMO

total orbital angular momentum Lowest Unoccupied Molecular Orbital

DAC

diamond anvil cell

n

refractive index

DED DMD

electric dipole strength magnetic dipole strength

N p

renormalisation coefﬁcient pressure

e

elementary charge

Rj , ϑj , ϕj ligand coordinates

Fk GK iQ

Slater parameters correlation crystal-ﬁeld parameters

S S

(k)

515

crystal-ﬁeld strength total spin angular momentum

555 556 559 559 562 562 563 567 572 577 580 582 583 583

516

T. TRÖSTER

SCCF

spin-correlated crystal ﬁeld

κ

isothermal compressibility

SRCM tk

symmetry-restricted covalency model power law exponent

Γ Γi

linewidth irreducible representation

W Z∗

transition rate effective nuclear charge

λ μ

wavelength crystal quantum number

α, β, γ

two-body conﬁguration interaction parame-

ν

wavenumber

αP

ters polarizability

ω τR

phonon frequency radiative lifetime

βR

branching ratio

ζ

spin-orbit coupling parameter

ε

dielectric function

Ω2,4,6

Judd–Ofelt intensity parameters

1. Introduction Ever since the foundations of spectroscopy were laid the problem of the relationship between the optical spectra emitted or absorbed by matter and the microscopic properties of the matter has been regarded as a fundamental problem. A class of very interesting systems with this regard is provided by non-metallic compounds of rare-earth ions with partially ﬁlled 4f shells. Their rich electronic structure is only weakly perturbed by the environment and provides a detailed ﬁngerprint of the surrounding arrangement of atoms and their interactions with the f-electrons. Valuable insight has been obtained by measuring the spectra of rare-earth ions in various host lattices. However, with respect to the relation of energy levels and host lattice structure, the presence of different ligands and local distortions around the impurity ion in each host lattice and the limited number of isostructural crystals available for spectroscopic studies restrict the empirical information thus obtainable. High pressure techniques, in contrast, offer a more powerful method for such studies. By applying pressure one can vary the interatomic distances continuously and thereby study the crystal structure dependence of the f-electron states directly. A second, equally interesting possibility is based on the different sensitivities of the energies of electronic states on interatomic distances. These speciﬁc sensitivities allows the experimentalist to alter the energy difference between two states and thus to get unique information about their mutual inﬂuence. The ﬁrst published work on the pressure dependence of optical spectra of solids seems to be of Paetzold (1940), who has studied the effect of pressure on absorption spectra of praseodymium nitrate, ruby, and other minerals between 1938 and 1939. To generate a maximum pressure of 0.1 GPa the samples were subjected to pressurised nitrogen. Using the same high pressure apparatus, Hellwege and Schröck-Vietor (1955) studied the pressure dependence of the absorption spectra of EuZn-nitrate. These authors, for the ﬁrst time, applied the crystal-ﬁeld Hamiltonian formalism for the analysis of the high pressure spectroscopic results. The development of a squeezer apparatus for optical studies by Drickamer and his coworkers (Fitch et al., 1957) and almost at the same time the development of the diamond anvil cell (DAC) (Weir et al., 1959; Jamieson et al., 1959) provided real breakthrough in the

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experimental study of lanthanide crystal ﬁelds under high pressure in general. Since then, different rare-earth ions in various compounds have been investigated and in many studies the pressure dependence of the crystal-ﬁeld and free-ion parameters were determined and interpreted. Recently, Bray (2001) has compiled several examples of luminescence properties of transition metal and lanthanide systems under pressure. The aim of this chapter is to present a review of the high pressure optical studies on rareearth ions in non-metallic compounds. Other methods, as for example neutron scattering, magnetic resonance techniques or Mößbauer spectroscopy will not be considered here, unless they provide additional valuable information to the optical studies. It will be demonstrated that the problem of host lattice structural dependence of 4fN states can be effectively tackled by high pressure techniques and hopefully the interest for further, more reﬁned high pressure studies of this problem can be stimulated. In the next section the rare-earth compounds that have been studied by optical means under pressure so far will be reviewed. Then, after a brief introduction of the most commonly used high pressure device, the diamond anvil cell, sect. 4 presents a discussion of the pressureinduced changes of the crystal-ﬁeld levels and their interpretation. In sects. 5 and 6 some aspects of the dynamical effects under pressure are discussed. These include lifetime and intensity measurements, the inﬂuence due to excited conﬁgurations and charge transfer bands, and the electron–phonon coupling.

2. High pressure technique A huge variety of different approaches to generate high pressures has been developed in the last century. In general, the devices depend on the type of materials under consideration (gas, liquid or solid), the desired temperature and pressure ranges, the pressure-generating mechanisms, and the experimental methods that are to be used. For detailed information about different types of high-pressure systems, the interested reader is referred to some very good text books and reviews dealing with various high-pressure techniques and methods (Eremets, 1996; Holzapfel and Isaacs, 1997). Roughly, one can distinguish between three different categories of high-pressure devices. Hydraulic systems are used for the compression of ﬂuids where the ﬂuid either acts as the sample itself or as a pressure-transmitting medium. The pressure range for these systems is usually limited to pressures below 2 GPa. Second, piston-cylinder devices are used for the compression of large-volume (> 1mm3) solid samples. Pressures of around 10 GPa are achievable with this method. The third and most important category contains all types of opposed-anvil systems. The underlying idea in this case is quite simple. Because pressure is deﬁned as force per area, a given force applied to the large sides of opposed conical anvils will result in an enlarged pressure between the small sides of the anvils. To reach very high pressures, the anvil material of course should be as hard as possible. Thus, starting in the 1970s, diamonds were used as the anvils which allowed for extending the pressure range up to several hundred GPa. At the same time, diamonds exhibit superior features as optical windows. They are transparent from

518

T. TRÖSTER

Fig. 1. Principle of the pressuregenerating method with opposed diamond anvils. The enlargement on the right side shows the central hole of the gasket ﬁlled with rubies, a sample, and a pressuretransmitting medium.

the far infrared to the vacuum ultraviolet and their intrinsic luminescence can be negligible when carefully selected. Meanwhile, the diamond anvil cell (DAC) has become the dominant device in high-pressure research. Although optical studies build up a big part of research performed with DACs, nearly every method used to study physical properties of matter has been successfully employed also in high-pressure DACs. Examples are electrical measurements (Gonzalez et al., 1986), X-ray diffraction (Hazen and Finger, 1982; Holzapfel, 1989), X-ray absorption (Tolentino et al., 1990), Mössbauer spectroscopy (Lübbers et al., 2000), neutron scattering (Vettier, 1989), resonance techniques (Sakai and Pifer, 1985). The principle of pressure-generation with opposed diamond anvils is shown in ﬁg. 1. A gasket with a central hole is placed between the two diamond tips to provide a sample chamber which can be ﬁlled with a pressure-transmitting medium to maintain hydrostatic conditions. Furthermore, the sample chamber is loaded with the sample and some pressure sensor. Different materials have been used for the gasket, depending on the maximum pressure desired and the experimental method to be employed. Common materials are all sorts of stainless steels, as for example Inconel X750. For pressures in the 100 GPa region, Re or Mo gaskets are used because of their higher strength. In the case of X-ray experiments, Be with its low atomic number has the advantage of low absorbance. The most common pressure sensor for optical studies is ruby (Al2 O3 :Cr3+ , Piermarini et al. (1975)), whose strong R1 and R2 luminescence line shifts under pressure have been calibrated up to 180 GPa at room temperature (Mao et al., 1978; Mao, 1989). At low temperatures the line position has to be corrected by a known temperature-induced shift (Noack and Holzapfel, 1979). Besides ruby also other sensors utilizing rare-earth ions have been proposed and discussed in literature (Shen et al., 1991). In most of these cases the pressure induced shifts of luminescence lines are used to determine the pressure (see sect. 4.5). One of the problems that has to be tackled in high pressure physics is the difﬁculty to provide truly hydrostatic or at least nearly hydrostatic conditions at very high pressure. In a DAC this requirement is fulﬁlled by the encapsulating ﬂuid. As soon as this ﬂuid solidiﬁes at a certain pressure, however, the pressure and stress distribution within the medium can become non-uniform. The same applies in the case of solids with low shear strengths, as for example

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519

Fig. 2. Intersection of a miniature diamond anvil cell (from Michael (2000)). The pressure range extends up to 35 GPa at room as well as at low temperatures. 1 – Screws for pressure generation, 2 – cell body, 3 – piston, 4 – adjustment screws, 5 – diamond support, 6 – diamond, 7 – tilting diamond mount hemisphere.

NaCl, which are sometimes used as the pressure transmitting medium. The unknown magnitude of the deviant stresses in such systems has often cast serious doubts on the interpretation of the measurements. Piermarini et al. (1973) have studied the hydrostatic limits of different liquids and solids by measuring the pressure gradient in the medium across the anvil diameter and observing the line shape of the R1 , R2 -lines of ruby. In the case of the line shape a broadening indicates local uniaxial components of the stress, due to its inﬂuence on the position of the lines. Thus, the broadening is a measure for the deviations from purely hydrostatic conditions. Other indicators for estimating the value of hydrostaticity are the splitting of the R1 and R2 lines of ruby and the lattice parameters of a crystal relative to the loading direction (Asaumi and Ruoff, 1986). The best medium with regard to hydrostatic conditions found by Piermarini et al. (1973) was a 4:1 methanol–ethanol mixture. In this case hydrostatic conditions were maintained up to a pressure of around 10 GPa. Other common media are a 16:3:1 mixture of methanol– ethanol–water with a hydrostatic limit of 14.5 GPa (Fujishiro et al., 1982), argon or neon with limits of 9 GPa and 16 GPa, respectively (Bell and Mao, 1981) or helium with a maximum value of 70 GPa (Eremets, 1996). A serious limitation is imposed to high-pressure experiments by the small size of the samples. Typical dimensions of the samples are in the range 200 × 200 × 40 μm. This small size causes weak signals and, especially in the case of absorption spectroscopy, it can be very difﬁcult or even impossible to study doped samples. Various types of DACs have been developed within the past decades. An overview of different cells is given for example by Jayaraman (1983). As an example to demonstrate the capabilities of DACs, ﬁg. 2 presents an cutaway view of a miniature cell used at the University of Paderborn. The cell was designed for magnetic resonance studies with maximum pressures of up to 35 GPa. To use it within magnetic ﬁelds, it is completely made of a non-magnetic Be–Co

520

T. TRÖSTER

alloy. The small size and mass permits the efﬁcient use also in standard cryostats. The support of the diamond anvils is made from boron carbide, a material which is nonconductive at low temperatures and allows the micro wave to enter the cell without signiﬁcant attenuation. 3. Survey of experimental data By far the largest part of the experimental results presented in this work, has been obtained with the aid of optical studies. Only in exceptional cases other methods, like electron-spin resonance or neutron scattering, have been employed to get information about energy levels under pressure. Obviously, these methods must be used in the case of non-transparent materials, where optical methods are not suitable. Before continuing, some words must be said with regard to the terms “rare earths” and “f elements” used in this chapter. The term rare earths includes the elements Sc, Y and the lanthanides La through Lu. However, this chapter solely deals with divalent or trivalent rareearth ions which are optically active, i.e., possess a partially ﬁlled f-shell. Thus, although the term rare earths is used in this chapter, it should be kept in mind that the elements Sc, Y, La, and Lu are excluded. In some exceptional cases the more general term f elements will be used, as for example when high pressure studies on actinide ions with a partially ﬁlled 5f shell are discussed. There are only few studies on 5f elements in non-metallic compounds under pressure, however, it seems interesting to compare the results found for these ions with those for the 4f-elements. To provide an overview of the rare-earth compounds which have been studied under pressure so far, table 1 lists the compounds, with respect to the doped ion and with the respective references. Obviously, Eu has been studied under pressure in much more host matrices than any of the other elements. This situation is similar to the observations made by GörllerWalrand and Binnemans (1996), who reviewed the experimental data on spectroscopic properties of trivalent lanthanide ions doped into crystalline host matrices at ambient pressure. They found that Nd and Eu alone built up around 50% of all studies. The optical studies performed on most samples of table 1 were aimed at different aspects of the f-electron properties. A considerable amount of the work was concerned with the energy level shifts under pressure. From these shifts, variations of free-ion parameters, crystal-ﬁeld parameters or crystal-ﬁeld strengths with pressure have been deduced. Other studies concentrated on changes in lifetimes or intensities, the efﬁciency of energy transfer between rare earths or rare earths and other impurities or on electron–phonon coupling effects under pressure. The various aspects investigated under high pressure will be presented within the next sections. 4. Energy levels 4.1. Theoretical background When an f-element ion is embedded in a crystal, the free-ion energy levels, characterized by the total angular momentum J , are affected in two different ways. On one hand the energy

OPTICAL STUDIES OF NON-METALLIC COMPOUNDS UNDER PRESSURE

521

Table 1 Non-metallic rare-earth compounds studied under high pressure. In almost all cases the energy level shifts as a function of pressure have been determined. The second column gives details concerning the measurements and evaluations made. In particular the following abbreviations are used: L: Luminescence-, A: Absorption-, E: Excitation-, S: Site-selective spectroscopy, O: Other methods, EPC: Electron–Phonon Coupling, Int: Intensities, LT: Lifetime, CFP: Crystal-Field Parameters, FIP: Free-Ion Parameters, IP: Intrinsic Parameters, ET: Energy Transfer Compound Ce3+ CaF2 :Ce3+ CeAs

Studies

Reference

A O

Ce(C2 H5 SO4 )3 ·9H2 O CeP

O, EPC O

Eu(C2 H5 SO4 )3 ·9H2 O:Ce3+ Y(C2 H5 SO4 )3 ·9H2 O:Ce3+

O, CFP O, CFP

Drotning and Drickamer (1973) Okayama et al. (1993), Yoshizawa et al. (1995), Oohara et al. (1995) Krygin and Prokhorov (1987a) Kohgi et al. (1993), Naka et al. (1994), Yoshizawa et al. (1995) Krygin et al. (1983), Krygin and Prokhorov (1984) Krygin et al. (1983), Krygin and Prokhorov (1984)

Pr3+ CaF2 :Pr3+ CeF3 :Pr3+ GdOCl:Pr3+ La(C2 H5 SO4 )3 ·9H2 O:Pr3+

L, CFP, IP A, FIP L, E, FIP, CFP, IP L, A, FIP, CFP, EPC

LaCl3 :Pr3+

L, A, E, Int, FIP, CFP, IP

LaOCl:Pr3+

L, E, FIP, CFP, IP

PrBr3 PrCl3

A L, A, Int, FIP, CFP, IP

Pr(C2 H5 SO4 )3 ·9H2 O

A, Int

PrF3 Pr(NO3 )3 ·6H2 O PrO2 PrOCl PrSb PrX (X = N, P, As, Sb, S, Se) SrF2 :Pr3+ YBa2 Cu3 O7 :Pr3+

A, Int A O L, A, FIP, CFP, IP O, CFP O L, CFP, IP O, EPC

Nd3+ Gd3 Ga5 O12 :Nd3+ Gd3 Sc2 Ga3 O12 :Nd3+ La(C2 H5 SO4 )3 ·9H2 O:Nd3+

L, O L, O O, CFP

Kennedy (1980), Kennedy and Campbell (1980) Voloshin and Krimnus (1977) Bungenstock et al. (2000a, 2000b) Voloshin and Krimnus (1977), Voloshin and Ivchenko (1980), Voloshin (1986) Keating and Drickamer (1961a), Gregorian and Holzapfel (1984), Urland et al. (1985, 1986), Gregorian et al. (1986, 1989, 1991), Voloshin (1988), Urland (1989), Tröster et al. (1993), Tröster (1999) Bungenstock et al. (1998, 2000b), Tröster and Holzapfel (1998) Wilmarth et al. (1989) Keating and Drickamer (1961a), Wilmarth et al. (1989), Tröster et al. (1993) Keating and Drickamer (1961a), Voloshin and Ivchenko (1980), Voloshin (1982), Krygin et al. (1984) Keating and Drickamer (1961a) Paetzold (1940) Hu et al. (1994) Bungenstock et al. (2000b) Vettier et al. (1977), Vettier (1989) Schirber et al. (1978) Kennedy (1980), Kennedy and Campbell (1980) Voloshin (1990)

Hua et al. (1996) Hua et al. (1996) Krygin et al. (1986), Krygin and Prokhorov (1987b) continued on next page

522

T. TRÖSTER Table 1, continued

Compound LaCl3 :Nd3+

Studies L, E, O, FIP, CFP, IP

LaF3 :Nd3+ NdBa2 Cu3 O7 NdBr3 Nd(C2 H5 SO4 )3 ·9H2 O NdCl3 ·6H2 O

L, FIP O, EPC A A, Int L, A, Int, FIP

NdCl3

L, A, Int, FIP, CFP, IP

NdF3 NdP5 O14 Pb2 Sr2 NdCu3 O8 Y3 Al5 O12 :Nd3+ YAlO3 :Nd3+ Y(C2 H5 SO4 )3 ·9H2 O:Nd3+ YP5 O14 :Nd3+

A, Int A, L, LT O, EPC L, O L O, CFP L, A, LT

Sm2+ BaF2 :Sm2+ BaFCl:Sm2+

L, CFP L, CFP, IP, EPC

CaF2 :Sm2+

L, A, CFP, EPC

CaFCl:Sm2+

L, O, CFP, IP

CsSmI3 SmFCl SmSe SmS SrB4 O7 :Sm2+

L A, X-ray O O L, E, LT

SrF2 :Sm2+

L, CFP, IP, EPC

SrFCl0.5 Br0.5 :Sm2+ SrFCl:Sm2+

L, LT L, Int, LT, FIP, CFP, IP

Sm3+ Chelates:Sm 3+ 49.5 H3 BO3 –49.5 LiF– 1.0 Sm2 O3

L, Int, ET L, LT

Reference Tröster et al. (1990, 1993), Gregorian et al. (1991), Krygin et al. (1992), Jayasankar et al. (1993), Tröster (1999) Voloshin et al. (1975) Goncharov et al. (1994) Wilmarth et al. (1989) Keating and Drickamer (1961a) Keating and Drickamer (1961a), Voloshin et al. (1975) Keating and Drickamer (1961a), Peterson et al. (1986), Tröster et al. (1993) Keating and Drickamer (1961a) Merkle et al. (1981) Goncharov et al. (1994) Hua et al. (1996), Hua and Vohra (1997) Barnett et al. (1973), Hua and Vohra (1997) Krygin et al. (1986), Krygin and Prokhorov (1987b) Merkle et al. (1981)

Kennedy (1980) Shen et al. (1990), Shen and Holzapfel (1993, 1995a, 1995c, 1995d, 1996), Shen and Bray (1998a, 1999) Wang and Drickamer (1973), Kennedy (1980), Kennedy and Campbell (1980) Oppenländer et al. (1989), Shen and Holzapfel (1995a, 1995b, 1995c, 1996), Shen and Bray (1998a, 1999) Chen et al. (1994c) Bolduan et al. (1985) Neuenschwander and Wachter (1990) Neuenschwander and Wachter (1990) Lacam and Chateau (1989), Leger et al. (1990), Urosevic et al. (1992), Datchi et al. (1997) Kennedy (1980), Kennedy and Campbell (1980), Yoo et al. (1991) Jovani´c (2001) Shen et al. (1990, 1991, 1997), Gregorian et al. (1991), Lorenz et al. (1994), Shen and Holzapfel (1995a, 1995c, 1995d, 1996), Jovanic et al. (1997a, 1997b), Shen and Bray (1998a, 1999)

Hayes and Drickamer (1982) Jayasankar et al. (2000), Lavin et al. (2002a) continued on next page

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523

Table 1, continued Compound Sm(C2 H5 SO4 )3 ·9H2 O Sm2 [Pt(CN)4 ]3 ·18H2 O Y3 Al5 O12 :Sm3+

Studies A, Int L, Int, ET L, Int

Reference Keating and Drickamer (1961a) Yersin and Stock (1982) Hess and Exarhos (1989), Bi et al. (1990), Hess and Schiferl (1990, 1992), Liu and Vohra (1993, 1994), Yusa et al. (1994)

Eu2+ BaBr2 Ba2 SiO4 :Eu2+ CaAl2 O4 :Eu2+ CaBPO5 :Eu2+ Ca2 P2 O7 :Eu2+ CdF2 :Eu2+ EuF2 EuO SrAl2 O4 :Eu2+ SrBPO5 :Eu2+ ZnS:Eu2+

L L, Int, LT L, Int, LT L, Int, LT L, Int, LT O, CFP A A, O L, Int, LT L, Int, LT L, Int

Tröster et al. (2002) Tyner and Drickamer (1977) Tyner and Drickamer (1977) Tyner and Drickamer (1977) Tyner and Drickamer (1977) Rewaj and Krupski (1980) Wang and Drickamer (1973) Zimmer et al. (1984) Tyner and Drickamer (1977) Tyner and Drickamer (1977) Wang et al. (1984)

L

Soga et al. (1988)

Eu3+ 90B2 O3 –10Na2 O– 1Eu2 O3 (glass) Ca(PO3 )2 :Eu3+ (glass) CaF2 :Eu3+

L, CFP, Int S, O, CFP

Chelates:Eu 3+ Eu[Au(CN)2 ]3 ·3H2 O Eu benzoylacetonate Eu2 O3

L, Int, ET L, Int, ET L, LT, Int, ET L, FIP

EuOCl Eu(OH)3 EuPO4 EuP5 O14 Eu2 [Pt(CN)4 ]3 ·18H2 O EuSe EuVO4 Eu2 Zn3 (NO3 )12 ·xH2 O EuZrF7 GdOBr:Eu3+ GdOCl:Eu3+ Gd2 O2 S:Eu3+ LaOBr:Eu3+

L, A, LT L, CFP L, LT, CFP L, LT, FIP, ET L, Int, ET O L A, CFP L L, FIP, CFP L, FIP, CFP L, FIP, CFP L, FIP, CFP

LaOCl:Eu3+

L, FIP, CFP, Int

Radli´nski and Silversmith (1986), Wright et al. (1995), Olsen et al. (1996) Hayes and Drickamer (1982) Yersin et al. (1998) Voloshin et al. (1976), Voloshin and Savutskii (1976) Chen et al. (1992b, 1992c, 1994b), Stump et al. (1993) Del Cul et al. (1991) Chen et al. (1994a, 1995) Chen et al. (1997) Huber et al. (1977), Blanzat et al. (1984) Yersin et al. (1979) Neuenschwander and Wachter (1990) Chen et al. (1994d) Hellwege and Schröck-Vietor (1955) Lavin et al. (2002b) Chi et al. (1997) Liu et al. (1998a) Chi et al. (1998a, 1998b) Chi et al. (1990), Wang and Bulou (1995), Shen and Holzapfel (1995a) Fonger and Struck (1970), Chi et al. (1986), Wang and Bulou (1993), Shen and Holzapfel (1995a) continued on next page

524

T. TRÖSTER Table 1, continued

Compound La2 O2 S:Eu3+

Studies L, LT, CFP

Na5 Eu(MoO4 )4 Na5 Eu(WO4 )4 Na2 O-2SiO2 :Eu3+ (glass) Y3 Al5 O12 :Eu3+ SrF2 :Eu3+ Y2 O3 :Eu3+ Y2 O2 S:Eu3+

L, CFP L, CFP L, S, LT, CFP, EPC L S L, LT L, Int, FIP, CFP

YVO4 :Eu3+

L, LT

Gd3+ CaF2 :Gd3+

A, O, CFP

Reference Fonger and Struck (1970), Webster and Drickamer (1980a, 1980b), Wang et al. (1992), Gleason et al. (1993) Guo et al. (1991) Guo et al. (1991) Lochhead and Bray (1995), Monteil et al. (2000) Arashi and Ishigame (1982) Wright et al. (1995) Jovani´c et al. (1996) Fonger and Struck (1970), Webster and Drickamer (1980a), Wang et al. (1984), Liu et al. (1988, 1998b), Nishimura et al. (1991) Chen et al. (1992a, 1992d)

O, CFP O, CFP O, CFP O, CFP

Wang and Drickamer (1973), Kasatochkin and Yakovlev (1977) Rewaj and Krupski (1978) Hayes and Drickamer (1982) Rewaj et al. (1992) Voloshin et al. (1976) Lukin et al. (1981) Rewaj et al. (1992) Rewaj et al. (1992) Rewaj et al. (1992)

Tb3+ CaF2 :Tb3+ Chelates:Tb 3+ La2 O2 S:Tb3+ TbP5 O14 Tb3+ in solutions Y3 Al5 O12 :Tb3+

A L, Int, ET L, E, Int, LT L, LT, CFP, ET L, Int, LT L, CFP

Drotning and Drickamer (1973) Hayes and Drickamer (1982) Gleason et al. (1993) Blanzat et al. (1984), Chi et al. (1988) Baumann and Bilal (1986) Liu et al. (1986)

Dy2+ CaF2 :Dy2+

A

Wang and Drickamer (1973)

A, Int

Keating and Drickamer (1961a)

L, CFP, IP, EPC O, CFP A, Int A, Int L, Int, ET

Kennedy (1980), Kennedy and Campbell (1980) Mesot et al. (1990) Keating and Drickamer (1961a) Keating and Drickamer (1961a) Takarabe et al. (1995, 1997), Takarabe (1996), Culp et al. (1997), Hogg et al. (1997a, 1997b) continued on next page

CdF2 :Gd3+ Chelates:Gd 3+ CsCaF3 :Gd3+ Gd benzoylacetonate La(C2 H5 SO4 )3 ·9H2 O:Gd3+ RbCaF3 :Gd3+ RbCdF3 :Gd3+ TlCdF3 :Gd3+

O, CFP L, Int, ET O, CFP

Ho3+ HoCl3 Er3+ CaF2 :Er3+ ErBa2 Cu3 Ox Er(C2 H5 SO4 )3 ·9H2 O ErCl3 GaAs:Er3+

OPTICAL STUDIES OF NON-METALLIC COMPOUNDS UNDER PRESSURE

525

Table 1, continued Compound GaP:Er3+ LiNbO3 :Er3+ Si:Er3+ SrF2 :Er3+

Studies L, E, Int, ET S, CFP L, Int, ET L, EPC

Reference Culp et al. (1996) Dierolf et al. (2000, 2003) Jantsch et al. (1996), Przybylinska et al. (1996) Kennedy (1980), Kennedy and Campbell (1980)

Tm2+ CaF2 :Tm2+ SrF2 :Tm2+ TmSe TmTe

A A O O

Wang and Drickamer (1973) Wang and Drickamer (1973) Neuenschwander and Wachter (1990) Neuenschwander and Wachter (1990)

Tm3+ Cs2 NaTmCl6 LiTmF4 TmCl3 Y3 Al5 O12 :Tm3+

O, EPC O, EPC A, Int L, ET

Mak et al. (2002) Kupchikov et al. (1982) Keating and Drickamer (1961a) Wamsley and Bray (1994a, 1994b, 1995), Shen et al. (2000)

Yb3+ InP:Yb3+

L, Int, ET

YbO YbS

A, O A, O

Stapor et al. (1991), Taguchi et al. (1994), Takarabe et al. (1994), Takarabe (1996) Syassen et al. (1985) Syassen et al. (1985)

levels are shifted to lower energies (a so-called red shift) and on the other hand the (2J + 1)fold degeneracy is partially or totally lifted. Although the term “crystal” has been used here, these effects are not restricted to crystals only. Any surrounding that breaks the spherical symmetry of the free ion can lead to a shift and splitting of the energy levels. Thus, the following considerations apply also to other materials like glasses or liquids where a longrange order does not exist. The ﬁrst step to calculate the energy levels of f-element ions is the calculation of the freeion energy levels. Within the central ﬁeld generated by the nucleus and the closed shells, all f-states are still degenerated. However, various interactions occurring in the f-electron system lead to a partial splitting of these states. The most important interaction is the Coulomb interaction, giving rise to terms characterized by the spin quantum number S and the angular momentum quantum number L. A further splitting occurs through the spin–orbit interaction which couples different terms and generates the 2S+1 LJ multiplets, where J denotes the total angular momentum. Due to the coupling of different terms, the quantum numbers S and L loose their meaning. However, because in most cases a large part of the intermediate coupled wavefunction is determined by one single term, the S–L-classiﬁcation is usually still preserved. In a phenomenological scheme the various interactions contributing to the Hamiltonian are split into unknown radial parts which are treated as adjustable parameters and the angular parts which can be calculated exactly. The matrix elements of the free-ion Hamil-

526

T. TRÖSTER

tonian HFI can then be written as follows: k F fk + ζ si li + αL(L + 1) + βG(G2 ) + γ G(R7 ) + T λ tλ |HFI | = k

+

k

i

P pk + k

λ

Mk mk .

(1)

k

The radial parts of the Hamiltonian which are treated as free parameters are represented by the Slater parameters F k (k = 0, 2, 4, 6) (Coulomb interaction), the spin–orbit coupling parameter ζ , two-body and three-body conﬁguration interaction parameters α, β, γ and Tλ (λ = 2, 3, 4, 6, 7, 8), respectively, the spin–spin and spin–other-orbit interactions parameters Mk (k = 0, 2, 4), and the electrostatically correlated spin–orbit interaction parameters P k (k = 2, 4, 6). The corresponding expectation values of the angular parts are denoted by fk , tλ , pk , and mk . li and si are the spin and orbital angular momentum of the ith electron, and G(G2 ) and G(R7 ) are the eigenvalues of Casimir’s operators for the groups G2 and R7 . For a detailed description of the free-ion Hamiltonian see, for example, Wybourne (1965) or Goldschmidt (1978). In the second step, the crystal-ﬁeld potential is introduced to the Hamiltonian. The potential in the one-electron approximation can be written as follows: HCF = (2) Bqk Cq(k) . k,q (k)

The Cq are tensor operators, whose matrix elements again can be calculated exactly, whereas the crystal-ﬁeld parameters Bqk are regarded as adjustable parameters. The number of parameters for this potential is greatly reduced by the parity and triangular selection rules and ﬁnally by the point symmetry for the f-element ion in the crystal. Detailed information about the crystal-ﬁeld potential has been given for example by Görller-Walrand and Binnemans (1996). Due to the so-called J -mixing within the crystal ﬁeld, multiplets with different J values are coupled. However, similar to the free-ion case, the levels are still designated by the principal 2S+1 L component of the crystal-ﬁeld wavefunction. For the further labeling of levels split by J the crystal ﬁeld, either the irreducible representation Γi (Bethe, 1929) to which the particular wavefunction belongs or the crystal quantum number μ deﬁned by Hellwege (1949) are most commonly used. The parametrization of the total Hamiltonian discussed above is utilized in almost all studies on energy levels of f elements in crystals at ambient as well as at high pressure. However, taking into account only the free-ion Hamiltonian from eq. (1), one already would have to determine not less than 20 parameters from the energy levels. Practically, this is not possible for the limited data sets available under pressure. Thus, in almost all cases only the most important Slater and spin–orbit coupling parameters in addition to the crystal-ﬁeld parameters have been determined. This procedure turned out to give an adequate description of the pressure-induced energy level shifts in most cases. In the following sections the effect of pressure on these parameters is presented. Extensions of the crystal-ﬁeld model towards relaxing

OPTICAL STUDIES OF NON-METALLIC COMPOUNDS UNDER PRESSURE

527

the one-electron approximation or including conﬁguration interactions will be considered in sects. 4.4.5 and 4.4.6. Before discussing the changes of free-ion and crystal-ﬁeld parameters, it should be mentioned that pressure in principle is not the most suitable quantity to characterize the observed changes. Actually, the cause for the increasing interaction strength under pressure is more directly related to the decreasing distances between f-electrons and ligands. Decreasing distances are related to a decreasing volume V which is related to pressure through the isothermal compressibility κ of the material: 1 ∂V κ =− (3) . V ∂P T Applying the same pressure to different materials results in different changes of the volume and distances. The larger κ, the larger will be the reduction of volume and thus the effect of pressure. Therefore, if a comparison of different materials is made, it is not appropriate to compare the pressure shifts, but one should compare them for the same changes of interatomic distances. 4.2. Line shifts In almost all cases, the absorption and luminescence lines of f elements shift to lower energies under pressure (one of the very few exceptions is presented in sect. 4.5 and ﬁg. 10). This general trend is caused by an overall contraction of the f conﬁguration and thus by a reduction in the energy difference between ground and excited state multiplets. This effect is related to decreasing Coulomb and spin–orbit interactions under pressure which will be discussed quantitatively in the next sections. Superimposed on the reduction in multiplet splittings is a change in their individual splittings. Usually, these crystal-ﬁeld splittings increase under pressure, however, in many cases also decreasing splittings have been observed. An example of observed line shifts for LaCl3 :Pr3+ is given in ﬁg. 3. In this case excitation spectra have been recorded up to around 8 GPa at 20 K (Tröster, 1994). The dominant red shift of the 3 H4 → 1 D2 transition lines and a slighter change in the respective splittings is clearly visible. The assignment of the various lines can be gathered from the energy level scheme schematically depicted on the right side of ﬁg. 3. The changes in the splittings are the reason for different shifts of transitions between the same two multiplets. From the line shifts, the corresponding variations of the energy levels can be derived. Thereby, the shift of the center of gravity (CG) of the 1 D2 multiplet with respect to the ground state 3 H4 (2) and the changes of the 1 D2 crystal-ﬁeld splittings with respect to the CG can be treated separately. The variations of the crystal-ﬁeld splittings of 1 D2 with respect to the CG are shown in ﬁg. 4. The CG shift of 1 D2 can be described by the polynomial function ECG = a0 + a1 p + a2 p2 with a0 = 16 730.4 cm−1 , a1 = −17.18 cm−1 /GPa, and a2 = 0.246 cm−1 /GPa2 . The total shift up to 8 GPa thus amounts to −122 cm−1 . Typical values for the observed red shifts of f-element transitions range between a few cm−1 /GPa and some tenth of cm−1 /GPa. The particular value strongly depends on the energy of the luminescent multiplet and the f element under consideration. Some characteristic

528

T. TRÖSTER

Fig. 3. Shift of the excitation line peaks of LaCl3 :Pr3+ under pressure at 20 K. The assignment of the lines can be gathered from the level diagram on the right side. CG denotes the center of gravity of the 1 D2 multiplet.

Fig. 4. Crystal-ﬁeld split levels of the 1 D2 multiplet of LaCl3 :Pr3+ under pressure, drawn with respect to the center of gravity ﬁxed to zero (dashed line).

OPTICAL STUDIES OF NON-METALLIC COMPOUNDS UNDER PRESSURE

529

Table 2 Selected average values for line shifts of different f elements under pressure. In all cases only the average linear coefﬁcient is given, slight deviations are neglected Ion Pr3+ Nd3+ Sm2+ Sm3+ Eu3+ Er3+ Tb3+ U3+

Host Transition 3P → 3H LaCl3 0 4 3P → 3H LaOCl 0 4 4 2D LaCl3 3/2 → I9/2 5D → 7F SrB4 O7 0 0 5D → 7F SrFCl 0 0 Y3 Al5 O12 Y1 5D → 7F EuPO4 0 0 5 D0 → 7 F 1 Y3 Al5 O12 4 4F LiNbO3 9/2 → I15/2 Y3 Al5 O12 5 D4 → 7 F6 4 2D LaCl3 3/2 ← I9/2

ν0 (cm−1 ) 20473.0 20267.8 21161.9 14589.8 14486 16189.1 17274.0 16932 15143.7 20146 15822.6

dν/dp (cm−1 /GPa) −22.9 −20.5 −11.2 −5.4 −22.4 −8.0 −2.1 −5.7 −2.8 −3.5 −65.3

Pressure range (GPa) 0–8 0–21 0–8 0–20 0–20 0–20 0–6 0–7 0–10 0–8 0–8

Reference 1 2 3 4 5 6 7 8 9 10 3

References 1. Gregorian et al. (1989) 2. Bungenstock et al. (1998) 3. Tröster (1994) 4. Lacam and Chateau (1989)

5. Shen et al. (1991) 6. Bi et al. (1990) 7. Chen et al. (1997)

8. Arashi and Ishigame (1982) 9. Dierolf et al. (2003) 10. Liu et al. (1986)

average values are summarized in table 2. The speciﬁc case of the actinide ion U3+ doped into LaCl3 has been included in table 2 to demonstrate the much larger shifts observable for this 5f element. This difference simply corresponds to the more extended 5f wavefunction with respect to the 4f wavefunctions of the lanthanides. 4.3. Nephelauxetic effect In sects. 4.1 and 4.2 the red shift of the free-ion levels due to either the incorporation of the f element into the crystal or due to the application of high pressure has been discussed. This effect is called nephelauxetic effect (Jørgensen and Reisfeld, 1977) and can be accounted for by a reduction of the free-ion parameters. Effectively, the transition from the free ion to the ion in the crystal can be thought of as increasing the spherically symmetric part of the crystal ﬁeld from zero to one. In high-pressure experiments, the interaction between the f-electrons and their environment and thus the spherically symmetric part of the crystal ﬁelds is increased further, which thus should cause a continued decrease of the free-ion parameters. Actually, this is what has been observed in all high-pressure experiments performed till now. Following these considerations, the high-pressure induced decrease of free-ion parameters is the same as the nephelauxetic effect and can thus be used to learn more about the nature of this effect. The reduction of the free-ion parameters has been ascribed to different mechanisms, where in general two types of models can be distinguished. On the one hand, one has the most often used wavefunction renormalisation or covalency models, which consider an expansion of the open-shell orbitals in the crystal (Jørgensen and Reisfeld, 1977). This expansion follows either from a covalent admixture with ligand orbitals (symmetry-restricted covalency mechanism) or from a modiﬁcation of the effective nuclear charge Z ∗ , due to the penetration of the ligand electron clouds into the metal ion (central-ﬁeld covalency mechanism).

530

T. TRÖSTER

The symmetry-restricted covalency model (SRCM) leads to: F k ∝ N 4

and ζ ∝ N 2 ,

(4)

where N is a renormalisation coefﬁcient, expressible as a sum including overlap integrals and covalency parameters (Newman et al., 1984). The central-ﬁeld covalency model (CFCM) predicts (Goldschmidt, 1978): F k ∝ Z ∗

and ζ ∝ Z ∗3 .

(5)

On the other hand, electrostatic models regard the ligands or the whole crystal as polarizable units and thereby lead to weaker Coulomb and spin–orbit interactions. In a dielectric screening model (DSM) from Morrison et al. (1967) the f element is placed within an empty sphere with radius RS which is embedded into an inﬁnite medium with dielectric constant ε. This leads to a reduction F k of the Slater parameters (Newman, 1973): F k =

(ε − 1)r k 2 2k+1 . k k+1 + ε RS

(6)

In most high-pressure experiments, only the covalency models have been taken into account. The likely reason for this is the arbitrary nature of the sphere radius RS used in the electrostatic model. One of the ﬁrst studies on the changes of free-ion parameters under pressure has been performed by Huber et al. (1977). They investigated the luminescence of EuP5 O14 up to 40 GPa at room temperature. From the energy level variations the change of the Slater parameter F2 and the spin–orbit coupling parameter ζ was determined, whereby the analysis was restricted to pressures below 10 GPa due to uniaxial stresses at higher pressures. According to their results, both free-ion parameters decreased under pressure, though the Slater parameter F2 showed a much weaker change than the spin–orbit coupling parameter ζ . This result supports the CFC model for the nephelauxetic effect. However, the quantitative results should be taken with some precaution because the theoretical analysis neglected contributions as for example intermediate coupling effects or J -mixing. A further system which has been studied under high pressure is R2 O2 S (R = Y, La, Gd) doped with Eu3+ . Wang et al. (1992) have measured the luminescence spectra of La2 O2 S:Eu3+ under pressures up to 13 GPa at room temperature. In the analysis of the observed energy level shifts, Wang et al. (1992) used the intermediate coupling wavefunctions and partly included J -mixing effects. The relative shifts of the Slater parameters Fk (k = 2, 4, 6) and the spin–orbit coupling parameter ζ up to 13 GPa were about −0.38% and −0.20%, respectively. Thus, the shift for the Fk parameters was twice as large as for ζ , which supports the SRC model, in contrast to the results for EuP5 O14 . Nearly identical results were obtained also for Y2 O2 S:Eu3+ (Liu et al., 1998a) and Gd2 O2 S:Eu3+ (Chi et al., 1998a, 1998b). In both cases the reduction of the free-ion parameters was about −0.40% for F2 and −0.20% for ζ up to pressures of 13 GPa and 14.8 GPa, respectively. Considering the two different covalency models, the authors concluded that the SRC model describes the nephelauxetic effect more reasonably than the CFC model.

OPTICAL STUDIES OF NON-METALLIC COMPOUNDS UNDER PRESSURE

531

The rare-earth trichlorides belong to the best studied systems at ambient as well as at high pressure. Voloshin et al. (1975) studied the effect of pressure on the free-ion parameters of NdCl3 ·6H2 O up to 2.3 GPa. They found reductions of −0.26%, −0.29%, −0.12%, and −0.25% for F2 , F4 , F6 , and ζ , respectively. Such variations can be explained neither by the CFC nor by the SRC model alone. In a study on LaCl3 :Pr3+ the corresponding changes up to 8 GPa were −1.2%, −0.6%, −0.7%, and −0.3% (Gregorian et al., 1986, 1989). It was pointed out that these changes could be described by the SRC but certainly not by the CFC model. However, Gregorian et al. (1989) discussed several weak points of the SRC model, which could not describe other experimental observations. One problem for example is, that the “nephelauxetic ratio” β = (Fk )complex/(Fk )free from which the so-called “covalency factors” are determined, is deﬁned to be independent of k, in contrast to the experimentally observed distinct differences in the relative decreases of F2 , F4 , and F6 parameters. Furthermore, ab initio calculations for Pr3+ in PrCl3 predicted that these covalency contributions are an order of magnitude too small to account for the reduction (Newman, 1973). In view of these problems, Gregorian et al. (1989) also considered the DS model. They assumed a proportionality between the spherical cavity radius RS and the mean Pr3+ –Cl− distance under pressure and found that up to about 70% of the change of the Fk could be accounted for by the 3% variation of this radius in the pressure range up to 8 GPa. Further high pressure studies concerning this problem have been performed on the compounds NdCl3 , LaCl3 :Nd3+ , PrCl3 , LaCl3 :Pr3+ (Tröster et al., 1993), and LaCl3 :U3+ (Tröster et al., 1995). The results for the changes in the free-ion parameters for these materials are summarized in table 3. The results for the pure material PrCl3 have larger uncertainties because of a very small data set available under pressure (Tröster et al., 1993). The actinide ion U3+ provides an interesting possibility to compare 5f with 4f elements and thus has been included in table 3. The essential quantitative differences to the lanthanide ion Nd3+ are due to the more extended 5f-wavefunctions and result mainly in smaller Coulomb interactions, a larger spin–orbit coupling and larger crystal-ﬁeld splittings. Corresponding to the more extended wavefunction, a larger shift of the energy levels is observed for U3+ , as mentioned already in the beginning of sect. 4.2. According to table 3 some trends which are valid for all these systems can be noted: (1) the shifts of the Slater parameters are larger or comparable to the shift of the spin–orbit coupling parameter, Table 3 Relative changes P /P of free-ion parameters (in %) for Nd3+ , Pr3+ (Tröster et al., 1993) and U3+ (Tröster et al., 1995) in different hosts up to a pressure of 8 GPa Parameter F 2 /F 2 F 4 /F 4 F 6 /F 6 ζ /ζ

LaCl3 :Nd3+ −0.7(1) −0.3(2) −0.4(1) −0.4(1)

NdCl3 −0.7(1) −0.4(2) −0.3(1) −0.3(1)

LaCl3 :Pr3+ −1.1(1) −0.8(2) −0.9(2) −0.4(1)

PrCl3 −2.0(4) −0.2(15) −3.9(17) −0.5(1)

LaCl3 :U3+ −6.6(8) −5.3(14) −3.2(19) −1.0(7)

532

T. TRÖSTER

Table 4 Experimental results for the Slater parameter reductions of Nd3+ , Pr3+ , and U3+ (Tröster et al., 1995) in LaCl3 under pressure up to 8 GPa in comparison with results from the dielectric screening model. All values in cm−1 Nd3+ Parameter F 2 F 4 F 6

Expt. −477 −204 −155

Pr3+ Calc. −298 −109 −150

Expt. −683 −398 −198

U3+ Calc. −323 −129 −195

Expt. −2622 −1766 −737

Calc. −659 −435 −750

(2) distinct differences in the shifts of the Slater parameters with different k are present, and (3) the total shift increases according to the order Nd3+ < Pr3+ U3+ . The last point is not very surprising because it proves that pressure effects are stronger the more extended the wavefunction is. Thus, the order Nd3+ < Pr3+ < U3+ simply reﬂects an increasing extension of the f-wavefunction. Point (1) can be explained if the SRC model is valid in these cases, because it predicts a stronger variation of the Fk compared to ζ . However, following the discussion by Gregorian et al. (1989), the SRC model has some drawbacks, for example it cannot explain the different shifts for different k parameters as noted in point (2). Tröster et al. (1995) also considered the DS model, whereby the radius RS was assumed to be proportional to a mean metal ion – chloride ion distance RM . As ambient pressure values they used ratios RS /RM of 0.417 for Nd3+ , 0.424 for Pr3+ , and 0.500 for U3+ . With these values the absolute changes of the Slater parameters have been calculated up to 8 GPa as shown in table 4. It must be emphasized that both the absolute values for the F k and the ratios F k /F k depend strongly on the choice of RS at ambient pressure. Nevertheless, it can be seen from table 4 that this simple model can partly produce shifts that are in the correct order of magnitude. However, these calculations can not be regarded as a deﬁnite prove for the relevance of the DS model since in fact a “true” value for RS could be completely different to the value used here, which then may result in even negligible shifts. Furthermore, the relatively large discrepancies for U3+ , where covalency effects can be expected to be especially important, indicate that precisely these cannot be disregarded. Similar to the rare-earth trichlorides, also different ternary MYX compounds have been studied thoroughly under high pressure. The results for the pressure-induced changes of the Slater parameter F 2 and the spin–orbit coupling parameter ζ of these and other compounds are presented in table 5. Due to the difﬁculties with the DS model, the evaluation of the parameter shifts has been performed only in terms of the two covalency models. Assuming small changes for the free-ion parameters, the relative changes were approximated by: Z ∗ N F k + = 4 Fk N Z∗

and

N Z ∗ ζ =2 +3 ∗ . ζ N Z

(7)

The ﬁrst parts are derived from the SRC model, the second parts from the CFC model. A useful quantity to distinguish both models is the covalency ratio CR (Bungenstock et al., 2000b): ! F k ζ CR = (8) . Fk ζ

OPTICAL STUDIES OF NON-METALLIC COMPOUNDS UNDER PRESSURE

533

Table 5 Relative decrease of the free-ion parameters F2 and ζ , the renormalisation factor N and the effective nuclear charge Z ∗ for Pr3+ , Nd3+ , Eu3+ , Sm2+ , and U3+ in different host lattices under pressures up to 8 GPa. The covalency ratio CR is a measure of the relative importance of the CFC or SRC models (see text). Rows 0–5 GPa, 5–10 GPa, and 10–15 GPa give the CR value of LaOCl:Pr3+ for different pressure regions Ion

Compound

Eu3+

LaOX (X = Cl, Br) LaOCl LaOBr GdOCl GdOBr Gd2 O2 S LaCl3 NdCl3 LaOCl 0–5 GPa 5–10 GPa 10–15 GPa PrOCl GdOCl LaCl3 MFCl (M = Ba, Sr, Ca) LaCl3

Nd3+ Pr3+

Sm2+ U3+

N/N (%) −0.03

Z ∗ /Z ∗ (%) −0.19

−0.16 −0.20 −0.05 −0.03 −0.06 −0.17 −0.18 −0.17

−0.14 −0.14 −0.09 −0.13 −0.02 −0.02 0.02 −0.09

Wang and Bulou (1995) Wang and Bulou (1995) Liu et al. (1998a) Chi et al. (1997) Chi et al. (1998a) Tröster et al. (1993) Tröster et al. (1993) Bungenstock et al. (1998)

−0.52 −0.46 −0.50 −0.39

1.07 1.14 0.79 0.56 1.44 1.75 2.33 1.28 1.22 1.48 1.99 1.74 1.95 2.00 3.00

−0.21 −0.23 −0.25 −0.31

−0.03 −0.01 0.00 0.08

Bungenstock et al. (2000b) Bungenstock et al. (2000a) Tröster et al. (1993) Shen and Holzapfel (1995a)

−1.00

6.60

−1.88

0.92

F 2 /F 2 (%) −0.31

ζ /ζ (%) −0.62

CR

−0.78 −0.96 −0.30 −0.26 −0.26 −0.70 −0.70 −0.77

−0.73 −0.84 −0.38 −0.45 −0.18 −0.40 −0.30 −0.60

−0.90 −0.91 −1.00 −1.17 −6.60

0.49

Ref. Shen and Holzapfel (1995a)

Tröster et al. (1995)

If only the CFC model is responsible for the decrease of the free-ion parameters, CR should be equal to 0.33, if only the SRC model is important, CR should be equal to 2. An intermediate value between 0.33 and 2 would indicate that both types of contributions are essential. According to table 5, in all cases except for some Eu3+ compounds, the decrease for F 2 is larger than for ζ . Thus, the SRC model plays the dominant role. In the case of some Eu3+ compounds on the contrary, the spin–orbit coupling parameter decrease more strongly than the Slater parameter, which leads to the conclusion that the CFC model is dominating here. The Eu3+ ion is, compared with Pr3+ , Nd3+ , Sm2+ , and U3+ , the ion with the least expanded 4f wavefunction. Therefore, one can conclude that the SRC model becomes increasingly more important when the wavefunction is expanded. This view is supported very strikingly by the data for U3+ , whose 5f wavefunction is much more expanded than the 4f wavefunctions of the other ions in table 5. For U3+ , the decrease of F 2 with respect to ζ is very large indicating that the classical CFC model does not play any signiﬁcant role anymore. These observations ﬁt also to the behavior in different pressure regions, as indicated in table 5 for the three regions 0–5 GPa, 5–10 GPa, and 10–15 GPa for LaOCl:Pr3+ . The increasing inﬂuence of the SRC model with increasing pressure is a consequence of the progressive expansion of the wavefunctions. The different values for the same ion in different host crystals also conﬁrm this general trend. For example, the sequence LaOCl:Pr3+ , PrOCl:Pr3+ , and GdOCl:Pr3+ of isostructural hosts corresponds to decreasing local distances around the Pr3+

534

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ion and thus to an increasing internal pressure. The wave functions of the f-electrons are thus expanding throughout this sequence, as shown by a decrease in the free-ion parameters at ambient pressure (Bungenstock et al., 2000b). Accordingly, the value CR increases from LaOCl:Pr3+ to PrOCl:Pr3+ and to GdOCl:Pr3+ and the same trend is observed also under pressure. An open question concerns some positive values for Z ∗ /Z ∗ listed in table 5. Positive values for this quantity are related to a value larger than two for CR. A value larger than two means, that even the SRC model cannot account for the much stronger changes in the Slater parameters with respect to the spin–orbit coupling parameter. These unusually strong changes can be described in the combined model only if the effective nuclear charge increases. It is not clear whether an increase in the effective nuclear charge is reasonable. In principle, such an increase could be explained by an increased covalency between the inner shell electrons and the ligands, leading to a charge transfer from inner shells to the ligands and thus to an increase of the effective nuclear charge Z ∗ for the f-electrons. This effect could be called “anti-screening”. On the other hand, if the effective nuclear charge does not change at all at high pressures, it would mean that the SRC model cannot describe the situation at strong compression or for strongly expanded wave functions. Some exceptions from the general trends have to be commented on. First, the results from Wang and Bulou (1995) are quite different to the results from Shen and Holzapfel (1995a) for LaOX:Eu3+ (X = Cl, Br). Although the value for CR found by Wang and Bulou (1995) is still lower than for all the other ions, it is distinctly larger than the value found by Shen and Holzapfel (1995a). One possible explanation is the fact that Wang and Bulou (1995) did not assume ﬁxed ratios for F4 /F2 and F6 /F2 but allowed the parameters to vary independently. However, because only two different terms, namely 5 D and 7 F have been observed under pressure, a large uncertainty is imposed on the parameters F4 and F6 , which was emphasized also by the authors. Thus, in principle only one Slater parameter can be determined. The pressure-induced variations of F4 and F6 found by Wang and Bulou (1995) are much smaller than the variation of F2 . This means, that a ﬁxed ratio would lead to a smaller variation of F2 which in turn would bring the CR values closer to the values from Shen and Holzapfel (1995a). Large values for CR are also found in the case of Gd2 O2 S:Eu3+ (Chi et al., 1998a). However, in this case the spin–orbit coupling parameter shows a strong nonlinear behavior with a steep drop in the beginning and a nearly constant value at higher pressures. The reason for this peculiar behavior was not addressed but should give rise to some care when using these values. An interesting improvement of the SRC model has been discussed by Wang and Bulou (1995). They considered simpliﬁed expansion factors used in the Hartree–Fock radial wavefunctions for the f-electrons. With these factors it was possible to introduce a k dependence for the pressure-induced change of different Slater parameters. This procedure would remove the weak point of the model which could not account for the observed k-dependence of the parameters under pressure.

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In summary, the analysis of the free-ion parameters of different materials under pressure have led to a coherent picture. The nephelauxetic effect can be described by a combination of the CFC and SRC models and depends on the expansion of the f-electron wavefunctions. Only at very high pressures or in the case of strongly expanded wavefunctions the SRC and CFC models could not provide a completely adequate description of the observed variations. 4.4. Crystal-ﬁeld splittings By far most work on the optical properties of the f shells under pressure concentrated on the mechanisms that cause the crystal-ﬁeld splittings of the free-ion levels. Whereas in the case of the nephelauxetic effect pressure always reduces the free-ion parameters and thus generates a red shift of the multiplets, it is not straightforward to explain how the crystal ﬁeld and thus the splittings change with increasing pressure. In principle, pressure moves the ions in the lattice closer to each other, which increases the interactions between the f-electrons and their ligands. Correspondingly, an increase of the crystal-ﬁeld splitting can be expected. In actual highpressure experiments, however, it was also observed that the crystal-ﬁeld splittings decreased with increasing pressure (see, for example, Bungenstock et al. (1998)). At ﬁrst glance such a result seems peculiar, but a closer look to the crystal-ﬁeld parameters introduced in sect. 4.1 reveals that not only the interaction strength of f-electrons and ligands but also structural information is contained therein. Actually, it is a change in the structural parameters which can be responsible for an overall decreasing crystal-ﬁeld strength, although the pure interactions between f-electrons and ligands monotonically increase with decreasing ion separations. In the following section the changes of the crystal-ﬁeld parameters and the crystal-ﬁeld strength under pressure is presented for various compounds. To extract the physical origin of the crystal ﬁelds, the subsequent sections will discuss the problem of local distortions, extract the structural information from the parameters by using the superposition model and ﬁnally relate the intrinsic parameters of this model to ab initio calculations. A last part will be devoted to the special case of glasses, where a strong inhomogenous broadening makes the evaluation of the data much more difﬁcult. 4.4.1. Crystal-ﬁeld parameters Crystal-ﬁeld parameters have been determined under pressure in a large amount of f-element compounds. Besides the optical methods, which have been employed in most cases, some work has been done using neutron scattering or magnetic resonance methods. These methods do not allow for the determination of more than the ground states, however, they can be used also in cases of non-transparent materials. For example, neutron scattering was used under pressure to study the high-TC compounds ErBa2 Cu3 Ox . In these materials charge redistributions in the CuO2 planes led to distinct changes of the 2nd order crystal-ﬁeld parameter under pressure (Mesot et al., 1990). A further example is a high-pressure study on PrSb, where it was demonstrated that a simple point charge model approach to the crystal-ﬁeld parameters appeared to break down (Vettier et al., 1977). Magnetic resonance studies have been performed in a number of different materials. In most cases the pressure dependence of the spin-Hamiltonian crystal-ﬁeld parameters have

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been determined, as for example for Gd3+ in ﬂuoroperovskite crystals (Rewaj et al., 1992), Gd3+ and Eu2+ in CdF2 (Rewaj and Krupski, 1978, 1980), and Eu2+ in CaF2 (Radli´nski and Silversmith, 1986). This method was also employed in the case of some ethylsulfate (ES) compounds, in particular for lanthanum ES doped with Gd3+ (Lukin et al., 1981), yttrium and europium ES doped with Ce3+ (Krygin et al., 1983), and yttrium and lanthanum ES doped with Nd3+ (Krygin et al., 1986). A much more detailed picture about the crystal-ﬁeld splittings and in turn about crystal-ﬁeld parameters is provided by optical means. In some cases much more than a hundred spectral lines can be observed and assigned at ambient pressure. The situation is usually worse in highpressure experiments because very small dimensions of the samples prevent the detection of weaker lines. In addition, pressure-induced broadening can lead to a strong overlapping and consequently to difﬁculties to resolve the lines. Nevertheless, in general the number of transitions and energy levels determined under pressure still exceed the number of crystalﬁeld parameters by far. Thus, in many studies the pressure dependence of the crystal-ﬁeld parameters was readily determined. In the previous section it was shown that the changes of the free-ion parameters within a common pressure range between atmospheric pressure and 10 GPa do not exceed a few percent. On the contrary, the changes of the crystal-ﬁeld parameters often are one or even two orders of magnitude larger within the same pressure range. For example, Chi et al. (1988) studied TbP5 O14 up to a pressure of 8 GPa. The site symmetry of the Tb3+ ion is C4ν , thus 5 crystal-ﬁeld parameters B02 , B04 , B44 , B06 , and B46 were considered. Their respective changes of the absolute values under pressure up to 8 GPa were 38%, 30%, 19%, 22%, and 89%. These changes demonstrate the strong effect of pressure in general and also the distinct differences for individual parameters. A well-known and thoroughly studied system at ambient as well as at high pressure is LaCl3 doped with various rare-earth ions. Anhydrous LaCl3 , as well as other lanthanide trichlorides, crystallizes in the hexagonal UCl3 type structure. The lanthanum ion is coordinated by 9 chloride ions arranged on a tricapped trigonal prism as illustrated in ﬁg. 5. The capping anions are referred to as equatorial, whereby an angle δ denotes the angular deviation of the equatorial ions from the normal to the prism faces. If δ is not equal to zero, the site symmetry of the lanthanide ion is C3h . However, in the case of LaCl3 δ is very small, therefore, an effective site symmetry D3h is commonly used. According to D3h symmetry, the crystal-ﬁeld potential can be written as:

(6) (2) (4) (6) (6) HCF = B02 C0 + B04 C0 + B06 C0 + B66 C6 + C−6 . (9) The pressure-induced variations of these crystal-ﬁeld parameters for LaCl3 :Pr3+ (Gregorian et al., 1989; Tröster et al., 1993) are represented in ﬁg. 6 by the solid lines. The dashed lines show the effects due to conﬁguration interaction. These effects will be discussed later in sect. 4.4.6. Further high-pressure studies on LaCl3 :Nd3+ (Tröster et al., 1990, 1993) and LaCl3 :U3+ (Tröster et al., 1995) were aimed at testing the transferability of crystal-ﬁeld parameter shifts for different f elements. In this series, the relatively simple 4f2 conﬁguration of Pr3+ is compared with the more complicated 4f3 conﬁguration of Nd3+ and the formally equivalent 5f3 conﬁguration of the actinide ion U3+ . Indeed the high pressure investigations for Nd3+ and

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Fig. 5. Coordination polyhedron of the Cl ligands around La in LaCl3 . RE and RA denote the equatorial and apical La–Cl bond distances. The angle Θ denotes the polar angle of the apical anions and δ the deviation from the normal to the prism faces of the equatorial anions (from Gregorian et al. (1989)).

U3+ in LaCl3 resulted in very similar shifts as those depicted in ﬁg. 6. In all cases the absolute values of B06 and B66 increased. Furthermore, the parameter B04 is the least affected parameter with a slight decrease in all cases. Distinct differences exist only for the parameter B02 , which shows a minimum for the lanthanides, but a simple increase for the actinide ion. Comparing only the two lanthanides, a very similar behavior under pressure could be established. In the case of U3+ at least the qualitative behavior, except for B02 , also matched that of the lanthanides. Quantitatively, the absolute shifts for the actinide ion were larger, a result that could be expected from the much more expanded wavefunctions of the 5f shell. It should be noted, however, that the relative changes were also very similar compared to the lanthanides. Further interesting and intensively studied systems are provided by MYX compounds. In particular, the crystal-ﬁeld parameters have been determined for ROY :Eu3+ (R = La, Gd; Y = Br, Cl), ROCl:Pr3+ (R = La, Pr, Gd) and MFCl:Sm2+ (M = Ba, Ca, Sr). For the corresponding references see table 1. As an example for these compounds, ﬁg. 7 shows the crystalﬁeld parameter shifts up to 16 GPa for ROCl:Pr3+ (R = La, Pr, Gd) obtained by Bungenstock et al. (2000b). The Pr3+ ion in ROCl is surrounded by four O2− and ﬁve Cl− ions. According to the site symmetry C4ν ﬁve crystal-ﬁeld parameters must be taken into account:

(4)

(6) (2) (4) (4) (6) (6) HCF = B02 C0 + B04 C0 + B44 C4 + C−4 + B06 C0 + B46 C4 + C−4 .

(10)

The qualitative as well as quantitative changes of the parameters shown in ﬁg. 7 are very similar in the three cases. Striking is the apparent continuation of the parameter shifts found for LaOCl:Pr3+ in PrOCl or GdOCl:Pr3+ . This behavior can be related to the fact that the doped Pr3+ ion is smaller than the replaced La ion in LaOCl. This causes a “negative” internal pressure compared to the pure substance PrOCl. Similarly, in GdOCl the Pr3+ ion is larger than Gd3+ , resulting in a “positive” internal pressure compared to PrOCl. The application of external pressure to LaOCl:Pr3+ then subsequently creates a structural environment similar to the ambient pressure environments of PrOCl and GdOCl:Pr3+ .

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Fig. 6. Variation of the crystal-ﬁeld parameters of LaCl3 :Pr3+ under pressure. Solid lines correspond to the conventional one-electron crystal ﬁeld, utilizing only the 4f2 wavefunctions as the basis set. δ denotes the mean deviation as deﬁned in the text. Dashed lines represent the results derived from the inclusion of the 4f1 5d1 conﬁguration interactions.

Although it is not possible to directly compare the individual crystal-ﬁeld parameters obtained for different hosts, it is possible to deﬁne an overall scalar crystal-ﬁeld strength S which is independent of the speciﬁc crystal structure. The strength parameter S can be calculated according to (Chang et al., 1982):

1/2 1 1 2 2 2 Bk0 S= (11) Bkq +2 + Bkq . 3 2k + 1 k

q>0

In a good approximation the maximum splitting of distinct 2S+1 LJ multiplets depends linearly on the crystal-ﬁeld strength. Due to enhanced interactions between f-electrons and ligands, S is expected to increase under pressure, a behavior, which indeed was found for many materials. Wang et al. (1992) have studied the crystal-ﬁeld strength for Eu3+ in La2 O2 S and found an increase from 314 cm−1 to 363 cm−1 up to 13 GPa. Similarly, for Y2 O2 S:Eu3+ an increase from 364 cm−1 to 395 cm−1 up to 10 GPa was noticed. In the case of YAG:Tb3+ S changed from 711 cm−1 at ambient pressure to 768 cm−1 at 8.2 GPa. A much stronger variation of the crystal-ﬁeld strength from 269 cm−1 at ambient pressure to 380 cm−1 at 5 GPa

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Fig. 7. Variation of the crystalﬁeld parameters and the crystalﬁeld strength of ROCl:Pr3+ (R = La, Pr, Gd) under pressure. The dashed lines show a superposition model calculation of the crystalﬁeld strength.

was observed for Na5 Eu(MoO4)4 (Guo et al., 1991). Although this simply seems to indicate distinct differences with respect to La2 O2 S or YAG, deﬁnite conclusions can be drawn only after the speciﬁc changes of the interatomic distances, due to the particular compressibilities, have been taken into account. Besides the crystal-ﬁeld parameter shifts, ﬁg. 7 also shows the variation of the crystal-ﬁeld strength for ROCl:Pr3+ . Obviously, the crystal-ﬁeld strength is distinctly decreasing in the case of LaOCl:Pr3+ up to 15 GPa and slightly decreasing for GdOCl:Eu3+ up to 10 GPa. The initial decrease for GdOCl:Eu3+ was observed also by Liu et al. (1998b). In addition, a similar behavior was found for LaOBr:Eu3+ up to 13 GPa (Chi et al., 1990) and GdOBr:Eu3+ up to 12 GPa (Chi et al., 1997). The possibility of a decreasing crystal-ﬁeld strength with increasing pressure has been mentioned in the beginning of sect. 4.4. There it was argued that a change in the structural parameters can occur in such a way that the overall crystal-ﬁeld strength decreases although the interactions between f-electrons and ligands increase with decreasing distances. This assumption is conﬁrmed by a calculation of the crystal-ﬁeld strength, shown by the dashed lines in ﬁg. 7. For the calculation, the superposition model (sect. 4.4.3) and the pressure-induced

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structural changes of the ROCl host lattices (Bungenstock et al., 2001) have been utilized. In the superposition model the crystal-ﬁeld parameters are calculated as a sum of products of so-called intrinsic parameters and geometrical factors. The intrinsic parameters represent the interactions between the f-electrons and one ligand and indeed were found to increase under pressure. However, the geometrical factors compensated this increase and in fact resulted in the calculated decrease under pressure. 4.4.2. Local distortions To relate the f-element spectra or equivalently the crystal-ﬁeld parameters to the structure of the host lattice, a detailed knowledge of the distances and angles of the atomic arrangement is required. In this respect, local distortions arising from a size mismatch between doped and substituted ions impose serious limitations on the determination of the parameter-structure relationship. Usually, at ambient pressure different hosts are used to generate different structural environments around the same f element. This enables the experimentalist to deduce a parameter-structure relation from the spectral data of the particular hosts. This procedure, however, suffers from the problem of unknown and in particular different local distortions for each host. On the other hand, parameter-structure relations determined from shifts under pressure are somewhat more reliable, because one and the same local distortion is present which in addition affects the parameter changes only if the distortions themselves considerably change under pressure. Nevertheless, the problem of local distortions cannot be neglected in highpressure experiments. Local distortions are present, if the distances or angles from the doped rare-earth ion to the ligands deviate from those of the pure sample. In principle, the whole information about the local distortions is contained in the spectra of the doped ions themselves. Thus, once the problem of the dependence of spectra on the distances is solved, it should be possible to derive the distortions directly from the spectra. The application of high pressure is directed towards the solution of exactly this problem, therefore high pressure could provide possibilities to determine local distortions. With these considerations in mind, Gregorian et al. (1989) proposed a model which allows to derive the local distortions for Pr3+ in LaCl3 from high-pressure experiments. The basic assumption of this model is that the local coordination polyhedra of the Pr3+ ion in two different host lattices with the same type of ligand complexes should be identical, as soon as all multiplet centroids of the Pr3+ ion are energetically equal in both hosts. To illustrate this method, ﬁg. 8 shows the dependence of the 3 P0 multiplet of Pr3+ in RCl3 (R = La, Pr, Nd, Gd) on the host lattice equatorial bond distances RE and apical bond distances RA (see ﬁg. 5) at ambient pressure (circles) as well as at high pressure for LaCl3 :Pr3+ (triangles). The structural data under high pressure have been determined by single-crystal X-ray diffraction studies (Gregorian et al., 1989). According to ﬁg. 8, the energies of the 3 P0 multiplet of Pr3+ in LaCl3 at 0.9 GPa and PrCl3 at ambient pressure coincide with one another. Simultaneously, the distances RE are equal in both lattices, but a distinct difference exists for the distance RA . However, according to the assumption that identical energies are synonymous with an identical local geometry, it must be concluded that the local distance RA

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Fig. 8. Energy of the 3 P0 multiplet of LaCl3 :Pr3+ as a function of the host lattice equatorial and apical La–Cl distances (from Gregorian et al., 1989). The circles correspond to the multiplet energies of Pr3+ in RCl3 (R = La, Pr, Nd, Gd) and the respective host-lattice bond distances at ambient pressure. Triangles denote the high-pressure data for LaCl3 :Pr3+ .

for Pr3+ in LaCl3 at 0.9 GPa is identical with the distance in PrCl3 at ambient pressure. Thus, the local distortion δRA can be simply read from the difference of the two host lattice values. The same considerations were used by Gregorian et al. (1989) to determine the local distortions for all structural parameters for LaCl3 :Pr3+ and for GdCl3 :Pr3+ . This model has been applied also for LaCl3 :Nd3+ (Tröster et al., 1993), ROCl:Pr3+ (R = La, Gd) (Bungenstock et al., 2000b). In both cases the optical high-pressure studies have been compared to results for the pure substances NdCl3 and PrOCl. A further possibility to derive local distortions can be based on models like the superposition model, which explicitly relate the crystal-ﬁeld parameters to structural parameters. This has been done for CaFCl:Sm2+ (Shen and Holzapfel, 1995b) and MFCl:Sm2+ (M = Ba, Sr, Ca) (Shen and Holzapfel, 1996). These results will be discussed in the next section. 4.4.3. Superposition model The crystal-ﬁeld parameters introduced in sect. 4.1 still contain all the structural information about the local environment. Therefore, a direct comparison of crystal-ﬁeld parameters derived from different hosts, even with the same site symmetry, is not reasonable. In addition, the crystal-ﬁeld parameters cannot be directly related to the distance and angle variations induced by the high-pressure application. Widely used models which extract the structural information from the crystal-ﬁeld parameters are the angular-overlap (Jørgensen et al., 1963) and superposition model (Bradbury and Newman, 1967). In the case of f elements, the superposition model has been employed widely for the analysis of crystal-ﬁeld parameters. The underlying assumption of the superposition model is that the one-electron crystal ﬁeld is additive and can be regarded as a superposition of the contributions from individual ions

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in the crystal. No speciﬁc assumptions are made on the kind of interactions between the felectrons and their ligands. Within this model, the crystal-ﬁeld parameters can be related to k and geometrical factors Kkq : so-called intrinsic parameters B k (Rj )Kkq (ϑj , ϕj ). Bqk = (12) B j

k depend only on the distance Rj and on the kind of ligand j located The intrinsic parameters B at (Rj , ϑj , ϕj ). The effect of pressure on the geometrical factors can be calculated once the structural changes under pressure have been determined for example by X-ray diffraction k a simple power law experiments. For the distance dependence of the intrinsic parameters B is commonly assumed: L

R0L tk kL R L = B kL R0L B (13) . RL L (R L ) and t L are treated as adjustable parameters and R L is a reference The quantities B k 0 k 0 distance that can be chosen arbitrarily. In principle, the number of ligand shells considered for the calculation of intrinsic parameters is not limited, however, it is usually assumed that only the nearest neighbors of the rare-earth ion contribute signiﬁcantly to the crystal-ﬁeld potential. Thus, especially long-range interactions like electrostatic interactions are not accounted for explicitly. Because these interactions are most important for k = 2 parameters, in many cases only the k = 4, 6 intrinsic parameters have been considered. At ambient pressure a large amount of work has been done to derive intrinsic parameters of rare-earth ions doped into different host crystals. For a detailed account of the superposition model and the ambient pressure results see, for example, Newman (1971), Newman and Ng (1989) and Garcia and Faucher (1995). According to eq. (13), the intrinsic parameters for a given ligand depend only on the distance between the rare-earth ion and the ligand. The determination of intrinsic parameters thus requires a variation of this distance, which naturally favors the application of high pressure. Despite this obvious possibility, only a limited number of intrinsic parameter studies under pressure has been published. This is simply explained by the number of different and partly sophisticated methods (optical spectroscopy, X-ray diffraction, extended X-ray absorption ﬁne structure) that must be employed simultaneously at high pressure to one and the same sample to get all the information necessary. The systems that have been studied in detail under pressure are LaCl3 doped with Pr3+ , Nd3+ (Tröster et al., 1995), and U3+ (Tröster et al., 1995), ROCl (R = La, Pr, Gd) doped with Pr3+ (Bungenstock et al., 2000b), and MFCl (M = Ba, Ca, Sr) doped with Sm2+ (Shen and Holzapfel, 1995c, 1995d). In the case of LaCl3 only one type of ligands exists and thus only one set of intrinsic parameters has to be determined. The results for this system for the Cl (R Cl ) and t Cl for Pr3+ , Nd3+ and U3+ are summarized in table 6. intrinsic parameters B k 0 k As can be seen from table 6 the crystal-ﬁeld strength for U3+ at ambient pressure, repreCl (R Cl ), is about twice as large as the value for the lanthanides. In spite of this sented by B k 0 remarkable difference, the distance dependences are nearly the same in all cases. The apparent difference in the case of t4 for LaCl3 :Nd3+ is either due to uncertainties in the determination

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Table 6 4,6 (R0 ) (in cm−1 ) and power law exponents t4,6 for chloride ligands for Pr3+ , Intrinsic crystal-ﬁeld parameters B Nd3+ , and U3+ in LaCl3 . R0 = 295 pm 4 (R0 ) B 287(22) 254(28) 507(47)

Pr3+ Nd3+ U3+

6 (R0 ) B 258(28) 271(32) 585(52)

t4 5(4) 2(4) 7(4)

t6 7(2) 6(2) 5(2)

Table 7 Intrinsic crystal-ﬁeld parameters (in cm−1 ) for chloride and oxygen ligands for Pr3+ in ROCl (R = La, Pr, Gd). Bqk represent special shifts for B04 and B44 R0Cl = 316 pm

Cl (R Cl ) B 2 0

t2Cl

Cl (R Cl ) B 4 0

t4Cl

Cl (R Cl ) B 6 0

t6Cl

B04

B44

LaOCl:Pr3+

906(26) 908(36) 898(84) O (R O ) B

5(2) 5(2) 5(2)

10(2) 13(2) 12(2)

351 205 150

327 226 190

t4O

181(43) 308(28) 298(43) O (R O ) B

11(2) 10(2) 9(2)

t2O

172(25) 189(28) 163(31) O (R O ) B

2229(177) 1819(189) 1607(70)

−1(1) −1(2) −1(2)

722(69) 705(47) 693(23)

8(3) 7(3) 9(2)

214(24) 272(50) 236(22)

12(2) 10(2) 11(3)

PrOCl:Pr3+ GdOCl:Pr3+ R0O = 235 pm

2

LaOCl:Pr3+ PrOCl:Pr3+ GdOCl:Pr3+

0

4

0

6

0

t6O

of the local distortions according to the model described in sect. 4.4.2 (Tröster et al., 1995) or to the neglect of correlation effects (see sect. 4.4.5). In contrast to the LaCl3 case, for ROCl two different ligands must be taken into account. In this host the Pr3+ ion is surrounded by four O2− and ﬁve Cl− ions. The four O2− ions are located in a plane below the central ion at a distance R O , four Cl− ions in a plane above the central ion at a distance RCl , and one Cl− ion above the Cl− plane at a distance RCl . Within the superposition model, the sum of the contributions from these ligands for the crystal-ﬁeld parameters Bqk can be written as: kO (RO )K O + 4B kCl (RCl )K Cl + B kCl (RCl )K Cl B0k = 4B k0 k0 k0 O (RO )K O + 4B Cl (RCl )K Cl . B k = 4B 4

k

k4

k

k4

and (14)

For every ligand (Cl and O) a set of three intrinsic parameters exists. The results for the intrinsic parameters determined from the crystal-ﬁeld parameter shifts up to 10 GPa are presented in table 7. Local distortions have been estimated according to the model described in sect. 4.4.2. Although only the immediate neighbors of the Pr3+ ion have been considered, the k = 2 parameters have also been derived by Bungenstock et al. (2000b). The results for these parameters, however, have to be taken with some precaution due to the problems of long-range interactions mentioned before. Within the estimated uncertainties, table 7 shows that a common set of intrinsic parameters for k = 6 can be found which describes all samples studied there. One remarkable difference Cl (R Cl ) for LaOCl:Pr3+ . However, this difference was caused is observed only in the case of B 6 0 simply by the use of different data sets in the determination of the crystal-ﬁeld parameters.

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Table 8 4,6 (R0 ) (in cm−1 ) and power law exponents t4,6 for chloride and ﬂuoride ligands Intrinsic crystal-ﬁeld parameters B for Sm2+ in BaFCl and SrFCl. R0 = 311.4 pm for chloride and R0 = 249.6 pm for ﬂuoride ions Sm2+ –Cl− Sm2+ –F−

4 (R0 ) B 124(14) 245(25)

t4 14(4) 6(2)

6 (R0 ) B 152(16) 172(18)

t6 10(3) 5(1)

Once identical data sets for all three samples were used, very similar values were also obtained Cl (R Cl ). for B 6 0 L . In that More serious difﬁculties were encountered in the case of the intrinsic parameters B 4 case two further parameters B04 and B44 had to be introduced into the ﬁtting procedure to get a reasonable description of the experimental crystal-ﬁeld parameters. The additional parameters represent pressure independent constants, added to the calculated crystal-ﬁeld parameters. Bungenstock et al. (2000b) discussed various possible sources of this problem and ﬁnally concluded that their high pressure data for hosts with two different ligands required modiﬁcations of the superposition model, possibly related to long-range electrostatic or ligand–ligand interactions which are not included in the model. Similar results were obtained by Shen and Holzapfel (1995d). They studied Sm2+ in BaFCl and SrFCl under pressures up to 8 GPa. The structure of both hosts is identical to LaOCl and thus eq. (14) can be applied also in this case, with the only difference of ﬂuoride ions replacing the oxide ions. The results for the k = 4, 6 intrinsic parameters for both types of ions are listed in table 8. When they compared their results with other literature values, they noted much larger tk exponents for the chloride but much smaller intrinsic parameters for the ﬂuoride ions. Shen and Holzapfel (1995d) argued that ligand–ligand interactions could remove Cl and simultaneously decreasing the values these discrepancies by increasing the values of B k F . They also pointed out that on the basis of some investigations for PrCl3 which included of B k ligand–ligand overlap effects (Curtis and Newman, 1970), one can expect contributions to the intrinsic parameters on the order of 10%. However, it would not be surprising if the interactions show up more strongly in systems like MFCl or LaOCl, where two kinds of ligands contribute to the crystal-ﬁeld parameters. Though some limitations of the superposition model have been revealed by the high pressure studies, in general a reasonable description of the crystal-ﬁeld parameters can be achieved. In particular this is the case when results for isostructural hosts are compared, where a common set of parameters usually is sufﬁcient to describe the pressure variations for all hosts. This fact has been used to derive local distortions for Sm2+ in CaFCl (Shen and Holzapfel, 1995b) and Sm2+ in BaFCl (Shen and Holzapfel, 1996). In both cases, the intrinsic crystal-ﬁeld parameters determined from a high-pressure study on SrFCl:Sm2+ were used as a starting point. In this sample, local distortions could be safely neglected due to the facts that the ionic radii of Sm2+ and Sr2+ are almost identical and the structural parameters for SmFCl and SrFCl are very similar. According to the superposition model the intrinsic parameters found for SrFCl:Sm2+ were simply transferred to either CaFCl:Sm2+ or BaFCl:Sm2+ . Then, combining the intrinsic parameters with crystal-ﬁeld parameters gained from optical high pressure studies on CaFCl:Sm2+

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and BaFCl:Sm2+ , it was possible to adjust the local structural parameters around the Sm2+ ion. As the result a shortening of the Sm2+ –Cl− and Sm2+ –F− distances by −7 pm and −6 pm in BaFCl (Shen and Holzapfel, 1996) and a lengthening by +3.4 pm and +3.5 pm in CaFCl (Shen and Holzapfel, 1995b) was found. These results are fully consistent with the expectation of shorter distances in BaFCl because of the smaller ionic radius of Sm2+ compared to Ba2+ and longer distances in CaFCl because of the larger ionic radius of Sm2+ compared to Ca2+ . As a last remark, it should be mentioned that also a few evaluations of the crystal-ﬁeld parameters of Pr3+ in LaCl3 in the scope of the angular overlap model have been made. Urland et al. (1985) and Urland (1989) used the angular overlap model to calculate the crystalﬁeld splittings of LaCl3 :Pr3+ under pressure. In addition, Gregorian et al. (1989) derived the parameters of both models and found that both approaches were capable to successfully describe the high-pressure results. 4.4.4. Ab initio calculations The intrinsic parameters discussed in the previous section open a practicable possibility to analyze the fundamental interactions occurring between the f-electrons and the ligands. In an ab initio calculation for the system Pr3+ –Cl− , Newman and Ng (1986) took into account ﬁve different mechanisms contributing to the intrinsic crystal-ﬁeld parameters at various Pr3+ – Cl− distances. These were point charges, charge penetration, exchange, p and s overlap, and p and s covalency. Gregorian et al. (1989) compared the theoretical results from Newman and Ng (1986) with their experimentally determined intrinsic parameters from a high-pressure study. They found Cl (R Cl ) at ambient pressure were signiﬁcantly smaller than the that the theoretical values B k 0 experimental values. However, the variation of the theoretical values agreed very well with the experimental results, especially if the large cancellations between the different theoretical contributions are taken into account. Following the approach suggested by Newman and Ng (1986), an improved ab initio calculation of the intrinsic crystal-ﬁeld parameters for the systems Pr3+ –Cl− (Shen and Holzapfel, 1994) and Nd3+ –Cl− (Shen, 1994) has been presented. The comparison of these results with experimental intrinsic parameters derived for LaCl3 :Pr3+ and LaCl3 :Nd3+ (Tröster et al., 1993) is shown in ﬁg. 9. Similar to the observations made by Gregorian et al. (1989), it is obvious that the ambient pressure values of the theoretical calculations are too small, yet the distance dependence is reasonably reproduced. Shen and Bray (1998b) also performed ab initio calculations of the intrinsic crystal-ﬁeld parameters for the systems Sm2+ –Cl− and Sm2+ –F− . Again the same formalism as in the case of the LaCl3 calculations was used. The calculated parameters were compared with experimental results from high pressure studies on MFCl:Sm2+ (M = Sr, Ba). The slight differences observed between theoretical and experimental parameters were attributed to the use of free-ion 4f wavefunctions, which are less expanded compared to the actual wavefunctions in the crystal (see sect. 4.3) and neglect of ligand–ligand and 4f5 5d1 conﬁguration interactions. Despite small deviations between the ab initio calculations and experimental high-pressure results, in general it can be noticed that the contributions considered in the calculations ac-

546

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Fig. 9. Ab initio calculations of the intrinsic parameters for the systems Pr3+ –Cl− (Shen and Holzapfel, 1994) and Nd3+ –Cl− (Shen, 1994). Dashed lines denote the individual contributions: CP – Charge Penetration, Ex – Exchange, PC – Point Charges, O – s, p Overlap, Co – s, p Covalency. $ marks the sum of all contributions. The experimental results were taken from table 7 (Tröster et al., 1993; Tröster, 1994).

count for the primary effects responsible for the crystal-ﬁeld potential. These observations point to the importance of overlap and covalency contributions and in addition justify the assumptions of the superposition model as reasonable approximations of the given situation. Finally, the interesting case of a negative exponent t2O found for the Pr3+ –O2− system (see table 7) in ROCl:Pr3+ (R = La, Pr, Gd) (Bungenstock et al., 2000b) should be mentioned. Shen (1994) also performed ab initio calculations for this system and in fact he found a negative value for t2O (for details, see Bungenstock, 1999). This agreement can be regarded as

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547

an interesting conﬁrmation of the ab initio calculations as well as the superposition model. However, these results should not be taken too seriously, because of the problems connected especially with the k = 2 parameters, as discussed in the previous section. In addition, the O (R O ) compared to same calculation produced a much too small ambient pressure value B 2 0 the experimental value. 4.4.5. Correlation crystal ﬁelds In sect. 4.1 the one-electron crystal-ﬁeld model for the fN conﬁgurations was introduced. Though this model is very successful in providing a description of the crystal-ﬁeld splittings, certain “anomalous” multiplets are poorly ﬁtted. Prominent examples are the 1 D2 multiplet of Pr3+ , the 2 H(2)11/2 multiplet of Nd3+ , and the 3 K8 multiplet of Ho3+ . Almost independent of the host crystal, the calculated crystal-ﬁeld levels of these multiplets show a much larger deviation from the experimental ones than all the other levels. Improvement of the crystal-ﬁeld splitting calculation has been achieved by two different approaches. On one hand the basis set of wavefunctions was extended to include also excited conﬁgurations. This approach will be dealt with in sect. 4.4.6. On the other hand, the oneelectron approximation has been relaxed to take into account electron correlation effects. The original formulation of the correlation crystal-ﬁeld parameterization has been proposed by Bishton and Newman (1968). Judd (1977) and Reid (1987) redeﬁned the operators to ensure their mutual orthogonality: (K) HOCCF = (15) GK iQ giQ . i,K,Q

As for the one-electron crystal ﬁeld, the GK iQ are treated as parameters, whereas the angular (K) can be calculated exactly. Again, the number of terms which have to be considered parts giQ can be reduced by the site symmetry. However, this number is much larger here than for the one-electron crystal ﬁeld. Actually, even for an octahedral site symmetry, 41 parameters are left, which cannot be determined from the experimental data. To tackle this problem, different approaches have been proposed. On one hand, it is possible to assume a certain type of interaction that is mainly responsible for the correlation effects. This leads to special correlations with less parameters, as for example the spin- or orbitally-correlated crystal ﬁelds or the δ-function model. For a more detailed description of such models see, for example, Reid and Newman (2000). On the other hand, a more practical approach is to analyze the various parameters with respect to their inﬂuence on the “anomalous” multiplets. According to this procedure Li and Reid (1990) could show that taking into account only the parameters G410AQ , a pronounced improvement for the description of the 2 H(2)11/2 multiplet of Nd3+ could be achieved. To study the dependence of correlation effects on the interatomic distances, Jayasankar et al. (1993) analyzed spectroscopic data for LaCl3 :Nd3+ at pressures up to 10 GPa. Using the su4 perposition model, they could derive the distance dependences of the intrinsic parameters B 4

and G10A which are multiplied by the same geometrical factor. In contrast to earlier assumptions (Reid, 1987), Jayasankar et al. (1993) could show that the correlation intrinsic parame-

548

T. TRÖSTER

ter changed much more with pressure than the one-electron intrinsic parameter. Assuming a power law dependence of the correlation intrinsic parameter, an exponent of t4OCCF ≈ 15, compared to a value of t4 ≈ 5 for the one-electron intrinsic parameter, was found. Another possibility to address the problem of the correlation crystal ﬁelds is an approach based on different wavefunctions for the spin-up and spin-down electrons. This spincorrelated crystal-ﬁeld model merely doubles the number of crystal-ﬁeld parameters and thus can be applied in most cases. Shen and Holzapfel (1995c) presented a high pressure study on spin-correlated crystal ﬁelds in MFCl:Sm2+ (M = Ba, Sr, Ca). In particular, they considered the splitting ratio R of the 5 D1 and 7 F1 multiplets, which should be equal to 0.298 within the conventional one-electron crystal-ﬁeld theory and independent of the host crystal. In a ﬁrst step, Shen and Holzapfel (1995c) considered ambient pressure as well as high pressure data of the isoelectronic Eu3+ ion. In this case they found a ratio of R = 0.238, which could be explained by taking into account a spin-correlated crystal-ﬁeld parameter c2 = −0.007(3). However, applying the same model to the high-pressure results for Sm2+ , extreme deviations were encountered. The authors attributed these deviations to a breakdown of the spincorrelated crystal-ﬁeld model for Sm2+ . As the reason for this failure, conﬁguration interactions with the 4f55d1 conﬁguration were determined. These interactions are expected to be much stronger for Sm2+ , because the energy of the excited conﬁguration is much lower (at about 20 000 cm−1 ) than in the case of Eu3+ (at about 50 000 cm−1 ). Recently, the δ-function model has also been employed to analyze high-pressure results on LaCl3 :Pr3+ and LaCl3 :Nd3+ (Burdick and Tröster, 2003). This model assumes the dominant contributions to the correlation crystal ﬁeld interactions arising from paired electrons within the same orbital. It has been shown that this model is capable to greatly improve the description of “anomalous” multiplets like the 1 D2 multiplet of Pr3+ at ambient pressure (Burdick and Richardson, 1997). Applying the model to the high-pressure data also distinctly improved the quality of the ﬁts for both samples and at all pressures. A striking example is the 1 D2 multiplet of Pr3+ , where the rms error rises from 14.8 cm−1 at ambient pressure to a maximum value of 20.1 cm−1 at 8 GPa, when using solely the one-electron crystal-ﬁeld parameters. On the contrary, if the δ-function model is included, a maximum rms error of only 0.9 cm−1 is found at ambient pressure and even smaller values are found at higher pressures. Furthermore, a very interesting property of these ﬁts concerns the one-electron crystal-ﬁeld parameter B04 of Nd3+ in LaCl3 . In this case large difﬁculties were encountered in deriving the 4 because of much too small variations of B 4 of only 1% from ambient intrinsic parameter B 0 pressure to 8 GPa (see sect. 4.4.3 and table 6). On the other hand, taking into account the δfunction model, the change of B04 distinctly increases to more than 10% from ambient pressure to 8 GPa. This clearly improves the values of the intrinsic parameter and points out the ability of the model to signiﬁcantly improve the energy level calculations. 4.4.6. Excited states High-pressure research on trivalent f elements is mostly concerned with the energy levels of the fN conﬁgurations. This is mainly due to the fact that the energies necessary to access higher-lying states are within the VUV region, where the diamonds start to absorb the ra-

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diation. The situation is much better in the case of divalent f elements whose excited states are much lower in energy. In principle, two different kinds of high energy states have been observed, on one hand charge transfer states, involving the excitation of an electron from a ligand orbital to the fN conﬁguration and, on the other hand, excited conﬁgurations of the f element itself, like the fN−1 d1 conﬁgurations. Besides the general interest on excited states, they can also strongly affect the properties of the f-electrons. For example, the two-body and three-body conﬁguration interaction parameters α, β, γ and Tλ (λ = 2, 3, 4, 6, 7, 8), which are used in the free-ion Hamiltonian describe the inﬂuence of excited conﬁgurations on the centroids of the fN multiplets. A further prominent inﬂuence of excited states is the interaction with fN−1 d1 conﬁgurations, which is accepted to be responsible for the observed intensities of f-f transitions. In the past, high pressure studies have been performed especially on the inﬂuence of the 4fN−1 5d1 conﬁgurations. After presenting these studies, a brief discussion about the few high pressure studies on charge transfer states will follow. The outstanding properties of f electrons stem from the fact that they are shielded from the crystal ﬁelds by outer closed sub-shells. For d electrons the situation is different, their wavefunction is much more expanded which causes a much stronger interaction with the lattice. Consequently, the 4fN−1 5d1 conﬁgurations show broad absorption and luminescence bands, in contrast to the sharp f-f transitions. The stronger interaction with the lattice also causes more pronounced pressure effects. Especially the energy shifts of the excited 4fN−1 5d1 conﬁguration are usually an order of magnitude larger than in the case of the f-electrons. Shifts of the luminescence lines from 4fN−1 5d1 → 4fN transitions are summarized in table 9. According to table 9 an average shift of the f-d conﬁguration can be determined to be around −130 cm−1 /GPa. This is approximately ﬁve times larger than the average shift of the f-f transitions which is on the order of −25 cm−1 /GPa. The f-d conﬁguration of U4+ shifts faster compared to the 4f elements, a result which is not unexpected if the already larger shift of the f-f transitions (see sect. 4.2) is taken into account. It is conspicuous that the excited conﬁgurations always shift to lower energies, with the only exception of CsSmI3 . In this sample, the f-d conﬁguration of Sm2+ is lower in energy than the 5 D0 multiplet and thus the luminescence is completely quenched at ambient pressure. However, at a pressure of 16.4 GPa Chen et al. (1994c) observed some new lines which they assigned to f-f transitions. According to this assignment the authors argued that the f-d conﬁguration must have shifted to energies above the 5 D0 multiplet to allow f-f transitions to become visible. However, from the results presented by Chen et al. (1994c) it is not quite clear whether the f-d conﬁguration really shows a continuous shift, because only a single spectrum recorded at 16.4 GPa is discussed. In addition, the authors assume a reversible ﬁrstorder phase transition to occur under pressure which of course could be made responsible for a discrete jump of the f-d conﬁguration. Thus, the positive value of the shift given in table 9 requires some further conﬁrmation. A similar effect as in the case of CsSmI3 has been observed by Yoo et al. (1991). In their study on the Sm2+ ions in SrF2 they could demonstrate an electronic crossover connected with a phase transition starting at pressures around 4.5 GPa. At this pressure, the f-d conﬁguration shifted below the 5 D0 multiplet.

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Table 9 Ambient pressure luminescence peaks and their pressure shifts for transitions from the 4fN−1 5d1 conﬁgurations to the ground state of the 4fN conﬁguration. Values marked with an asterisk correspond to the onset of the lowest energy luminescence line. In the case of UO2 , excitation energies were determined Ion Ce3+ Pr3+ Sm2+

Ground State 4f 1 4f 2 4f 6

Host CaF2 LaOCl CaF2

Eu2+

4f 7

Dy2+

4f 10

CsSmI3 SmFCl SrF2 BaBr2 Ba2 SiO4 CaAl2 O4 CaBPO5 Ca2 P2 O7 EuF2 CaF2

Tm2+

4f 13

CaF2 SrF2

U4+

5f 2

UO2

E (cm−1 ) 32900 45000 16100 23500 35150 12500∗ 16600∗ 14800∗ 24700 19600 22900 24800 23300 30300 14000 17250 21800 35500 16850 24400 17500 24850 20160

Shift (cm−1 /GPa) −143 −30∗ −113 −106 −113 +200∗ −200∗ −149∗ −225 −127 −290 −150 −70 −175 −156 −138 −94 −119 −106 −119 −100 −150 −282

Pressure range (GPa) 0–7 0–10 0–8 0–8 0–8 0–16 0–9 0–13 0–10 0–10 0–10 0–10 0–10 0–8 0–8 0–8 0–8 0–8 0–8 0–8 0–8 0–8 0–15

Reference 1 2 3 4 5 4 5 6 7 8 8 8 8 3 3 3 3 3 3 3 3 3 9

References 1. Drotning and Drickamer (1973) 2. Tröster and Holzapfel (1998) 3. Wang and Drickamer (1973)

4. Chen et al. (1994c) 5. Bolduan et al. (1985) 6. Yoo et al. (1991)

7. Tröster et al. (2002) 8. Tyner and Drickamer (1977) 9. Syassen et al. (1986)

Apart from the interest in the properties of the excited conﬁgurations themselves, their inﬂuence on the f-electrons has been studied extensively. As mentioned in the beginning of this section, mixing with excited conﬁgurations is responsible for the observed intensities of f-f transitions. This feature will be discussed in sect. 5.3.1. The inﬂuence on the center of gravity of the multiplets is also taken into account in most studies via the two-body and three-body conﬁguration interaction parameters. However, relatively new is the inclusion of excited conﬁgurations to improve the description of the crystal ﬁeld split levels within the f conﬁguration. In this respect, it was demonstrated for example for Pr3+ (Garcia and Faucher, 1989) and Nd3+ (Faucher and Moune, 1997), that the crystal-ﬁeld level calculations both in general and for the “anomalous” multiplets, could be greatly improved by taking into account the 4fN−1 5d1 and 4fN−1 6p1 conﬁgurations. The effects due to conﬁguration interactions are speciﬁcally interesting for high-pressure experiments because the large red shift of the excited conﬁgurations should lead to a distinct increase in the interactions.

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551

In sect. 4.4.1 the pressure-induced variations of the crystal-ﬁeld parameters of LaCl3 :Pr3+ were shown in ﬁg. 6. In this case the “anomalous” multiplet 1 D2 could also be measured under pressure (Tröster et al., 1993), which opened a possibility to study the conﬁguration interactions as a function of pressure. Including the 4f15d1 conﬁguration in the energy level ﬁts and leaving only the energy distance to the 4f2 conﬁguration as an adjustable parameter, the mean deviation δ decreased from around 8 cm−1 to less than 4 cm−1 at ambient pressure (Tröster and Holzapfel, 2002). Furthermore, the observed increase of δ under pressure completely vanishes (see ﬁg. 6). The mean deviation is deﬁned as: " (ECalc. − EExp. )2 , δ= (16) N where N is the number of energies measured. The energy distance between both conﬁgurations was found to decrease with increasing pressure, however, the rate of around 1000 cm−1 /GPa seems to be too large compared to the typical values given in table 9. Nevertheless, this basically reasonable behavior points to the importance of conﬁguration interactions also for the energies of the 4f2 levels. It should be stressed that the conventional crystal-ﬁeld parameters within the f-conﬁguration partly show distinct changes when including the conﬁguration interaction. The strongest deviation is found for B04 , where a distinct pressure-induced change of its value is observed only if the conﬁguration interaction is taken into account (see ﬁg. 6). This behavior is very similar to what was observed in the case of the δ-function model as discussed in sect. 4.4.5 and may also remove the difﬁculties encountered for the determination of the k = 4 intrinsic parameters. Further high-pressure studies on conﬁguration interactions have been performed for LaOCl:Pr3+ taking into account the 4fN−1 6p1 conﬁguration (Bungenstock, 1999) and LiYF4 :Pr3+ taking into account the 4fN−1 5d1 and 4fN−1 6p1 conﬁguration (Tröster and Lavin, 2003). In both cases distinct improvements of the rms deviations at ambient as well as at high pressures have been obtained. The absolute values of the crystal-ﬁeld parameters within the 4f conﬁguration changed up to 50%, however, their pressure variations showed only minor differences. The only system that has been studied in some detail with respect to charge transfer states under pressure is R2 O2 S:Eu3+ (R = La, Y). Webster and Drickamer (1980a) observed a blueshift of the absorption maximum of the charge transfer band in La2 O2 S:Eu3+ with a rate of approximately 200 cm−1 /GPa. The charge transfer state is believed to be formed here with the transfer of an electron from the sulﬁde S2− to the Eu3+ ion. The shift of the charge transfer state in Y2 O2 S:Eu3+ was found to be larger than in La2 O2 S:Eu3+ with a rate of approximately 250 cm−1 /GPa. Further studies on these bands by Wang et al. (1984) and Gleason et al. (1993) mainly concentrated on the inﬂuence on the intensities and lifetimes of the f-f transitions. These effects will be discussed in sect. 5.3.2. The inﬂuence on the energy levels within the f conﬁguration was not addressed.

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4.5. Pressure sensors The line shifts of f-f transitions discussed in sect. 4.2, offer an interesting possibility to establish high pressure gauges. As mentioned in sect. 2, ruby is still the most widely used gauge for pressure determination. However, some deﬁciencies caused a continuous search for improved sensor materials. Especially the temperature induced broadening and quenching limits the application of ruby to below 500 ◦ C. New sensors should solve this problem, but at the same time should still preserve the advantages of ruby, namely the strong luminescence efﬁciency and the strong line shift with increasing pressure relative to the given linewidth. Some general requirements for a luminescence pressure sensor can be formulated as follows: • the lines should show a large shift with pressure (measure: dλ/dp), • the temperature dependent line shift should be as small as possible (measure: dλ/dT ), • for high sensitivity and precision, the linewidth Γ should be small compared to the line shift (measure: Γ −1 dλ/dp), • the spectrum should consist of a single line, • no signiﬁcant broadening or weakening of the line should occur. Due to these requirements, special attention has been paid to rare-earth sensors because the shielding of the f-electrons produces very sharp lines which are less sensitive to the environment compared to the 3d electrons of Cr3+ . One of the ﬁrst studies taking into account rare-earth ions as a pressure sensor by Barnett et al. (1973) used Nd3+ doped into YAlO3 . The pressure coefﬁcients dλ/dp and temperature coefﬁcients dλ/dT were compared there for several potential luminescence sensors up to 10 GPa. As expected, the temperature shift of the R2 → Z2 line at 875.3 nm, belonging to the 4 F3/2 → 4 I9/2 transitions of Nd3+ (for the nomenclature see, for example, Dieke, 1968), was indeed approximately an order of magnitude smaller than for the Cr3+ doped samples. However, at the same time the pressure coefﬁcient for Nd3+ was found to be much smaller. As shown in sect. 4.2, in almost all cases of rare earth doped compounds a red shift of the optical transitions is observed, due to decreasing spin–orbit and Coulomb interactions under pressure. However, in the case of Nd3+ doped into YAlO3 , Barnett et al. (1973) observed a blue shift of the 4 F3/2 → 4 I9/2 transitions. This peculiar behavior was taken up by Hua and Vohra (1997), who studied the 4 F3/2 → 4 I9/2 transitions in the same host YAlO3 as well as in Y3 Al5 O12 (YAG) in the extended pressure range up to 80 GPa. From the observed line shifts they deduced the energies of the two crystal-ﬁeld levels of 4 F3/2 , R1 and R2 , as a function of pressure as shown in ﬁg. 10. Corresponding to the blue shift of the luminescence lines, both levels showed a continuous shift to higher energies in YAlO3 , in contrast to the case of YAG, where both levels shift to lower energies, as expected. Hua and Vohra (1997) did not give an explanation why the levels in YAlO3 behave completely different to what is usually observed. In principle, the observed blue shift of these levels point to increasing Coulomb and spin–orbit coupling interactions, which should be connected with an increasing local volume (see also sect. 4.3). Whether such a behavior is reasonable or not could be answered only by further investigations as for example using

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553

Fig. 10. Effect of pressure on the 4F 3/2 crystal-ﬁeld levels in YAlO3 and Y3 Al5 O12 . The solid lines are polynomial ﬁts to the data (from Hua and Vohra (1997)).

high-pressure X-ray diffraction studies. In any case, Hua and Vohra (1997) noted that the 4F 4 3/2 → I9/2 transitions may be suitable as a pressure gauge in diamond anvil research at ultrahigh pressure. One of the main advantages of this system is that there is no interference with the diamond luminescence as in the case of ruby above 100 GPa. A further requirement for a pressure sensor is the stability of the host lattice at high pressures and temperatures. This requirement strongly narrows the range of possible candidates for high-pressure sensors. From X-ray diffraction experiments under pressure, it was found that YAG is stable at least up to 69 GPa at room temperature (Liu and Vohra, 1993). This is one of the reasons why doped YAG was chosen by many researchers as a promising host for pressure calibrants. One of the best studied sensor material is YAG doped with Sm3+ , whose most intense luminescence feature is a doublet at 16 186.5 cm−1 and 16 231.5 cm−1 (Y1 and Y2 lines). This doublet has been studied at room temperature up to a maximum pressure of 180 GPa (Bi et al., 1990; Yusa et al., 1994; Liu and Vohra, 1994) and it was found that the pressure-induced peak shift is comparable to the R1 shift of ruby. At the same time, the temperature-induced shift is almost two orders of magnitude smaller than the observed shift for the R1 peak. In fact, measurements at elevated temperatures up to 900 ◦ C and 10 GPa (Hess and Exarhos, 1989; Hess and Schiferl, 1990) as well as studies at temperatures above 400 ◦ C up to 25 GPa, indicated that the pressure could be determined from the Sm3+ luminescence without any temperature correction in this range (Hess and Schiferl, 1992). Besides the Sm3+ ion, the Eu3+ ion was also studied in YAG (Arashi and Ishigame, 1982). In this case the 5 D0 → 7 F1 transitions were monitored up to a temperature of 700 ◦ C and a pressure of 7 GPa. The results for the temperature and pressure-induced line shifts were

554

T. TRÖSTER Table 10 Selected characteristic values for different pressure sensors. Values in parentheses are estimated

Material

Cr3+ :Al2 O3 Cr3+ :YAlO3 Nd3+ :YAlO3 Eu3+ :YAG Sm3+ :YAG Sm2+ :SrB4 O7 Sm2+ :SrFCl

Transition

λ(nm)

dλ/dp (nm/GPa)

dλ/Γ dp (1/GPa)

dλ/dT (nm/103 K)

2E → 4A

694.2 722.8 875.3 590.6 617.8 685.4 690.3

0.365 0.70 −0.13 0.197 0.30 0.255 1.10

0.49 0.7 −0.065 (0.8) 0.23 1.7 5.8

6.8 7.6 0.001 −0.54 0.23 −0.1 −2.3

2E → 4A

2 2

4 3/2 → I9/2 5D → 7F 0 1

4F

Y1 5D → 7F 0 0 5D → 7F 0 0

(dλ/Γ dp) /(dλ/dT )103 K /nm GPa 0.072 0.092 65 0.002 1 17 2.5

Reference

1 1 1 2 3 4 5

References 1. Barnett et al. (1973) 2. Arashi and Ishigame (1982)

3. Hess and Exarhos (1989) 4. Lacam and Chateau (1989)

5. Shen et al. (1991)

similar to YAG:Sm3+ . However, the two strongest lines in the luminescence spectrum were approaching each other with increasing pressure, resulting in a strong overlap and thus an increased error in the line position determination already at 6 GPa. Another luminescence sensor, SrB4 O7 :Sm2+ has been suggested by Lacam and Chateau (1989). The advantage of using Sm2+ instead of Sm3+ is the occurrence of the well-isolated singlet transition 5 D0 → 7 F0 at 685.41 nm at ambient conditions. Also in this case the pressure-induced shift was similar to ruby, whereas the temperature-induced shift was much smaller. The stability of the host was proven up to 108 GPa (Leger et al., 1990) and the shift of the 5 D0 → 7 F0 transition has been calibrated in a hydrostatic medium (helium) up to 124 GPa (Datchi et al., 1997). Another promising material is SrFCl:Sm2+ . Shen et al. (1991) and Lorenz et al. (1994) have studied the pressure-induced shift of the 5 D0 → 7 F0 transition of the Sm2+ ion up to 20 GPa at room temperature and determined also the temperature-induced line shift up to 370 ◦ C at ambient pressure. According to these studies the line shift under pressure is approximately three times larger than for ruby. At the same time, the temperature dependence was found to be about three times smaller. From the point of view of sensitivity SrFCl:Sm2+ is the best sensor studied so far. However, the main drawback here is the intensity decrease under pressure, which is due to an enhanced interaction of the 5 D0 energy level with the 4f5 5d1 conﬁguration. The decrease already starts at around 10 GPa, limiting the use of this sensor to this lower pressure range. Some characteristic values of the pressure sensors mentioned here have been summarized in table 10. As mentioned before, the value Γ −1 dλ/dp, denoting the sensitivity of the sensor with respect to a pressure change, is the highest for SrFCl:Sm2+ . However, if an experiment requires high pressures and high temperatures, a closer look at the value of Γ −1 dλ/dp/(dλ/dT ) is necessary. This value can be regarded as a measure for the overall performance of the sensor with respect to pressure and temperature. From this point of view YAlO3 :Nd3+ would be the best sensor due to its extremely low temperature shifts.

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4.6. Structural probes In many cases the crystal structure of a rare-earth compound studied under high pressure is a priori known. In such studies the quality of the theoretical link between structure and spectra can be tested. However, a different possibility would be to use the experimentally determined spectral variations in connection with a theoretical approach to derive information about the local structure of the rare-earth ions. Such an attempt has been made in sect. 4.4.2, where the local distortions have been derived either directly from the spectra or by applying the superposition model. Similarly, high pressure studies have been used to get information about the structure in more complicated cases of multiple sites or glasses. In addition, the spectra of rare-earth ions have been used to detect phase transitions that often occur under pressure. Results of such studies will be discussed in the next two sections. 4.6.1. Multiple sites/glasses The high pressure studies presented so far only considered compounds with a single, welldeﬁned site for the rare-earth ion. However, in contrast to this case, many materials exhibit either a discrete variety of different sites or even a continuous distribution of sites, a situation typically encountered in glasses. In the case of different, but spectroscopically still resolvable sites, it is possible to study the effects of pressure on each individual site. Such an attempt has been made by Dierolf et al. (2000) for Er3+ ions doped into stoichiometric LiNbO3 . In this case a special spectroscopic technique, a combined excitation-emission spectroscopy, allowed to observe the pressure shifts of slightly different sites. From the shifts, the variations of the crystal-ﬁeld parameters could be determined. These variations include all the information necessary to derive characteristics of the structure of each site (Dierolf et al., 2003). Also in the case of semiconductors rare-earth ions often occupy different sites. For example, in GaAs at least 10 different types of Er3+ centers can be present simultaneously within the sample (Wolford and Bradley, 1985). Hogg et al. (1997a, 1997b) have studied the luminescence spectra of different Er3+ centers under hydrostatic pressures. They recognized some new centers which became optically active under pressure. In addition, it was shown that one center exhibited a conﬁgurational change at an elevated pressure (Hogg et al., 1997a). Further work mainly concentrated on high-pressure effects on glasses doped with f elements. Soga et al. (1988) investigated densiﬁed glass specimens of 90 B2 O3 –10 Na2 O– 1 Eu2 O3 obtained by applying pressures up to 6 GPa. They noted that pressure ﬁrst eliminates the atomic scale voids, usually appearing when the glass is quenched from high temperatures. Above 2 GPa no voids were formed during the quenching process. Furthermore, the ﬂuctuation of local ﬁelds around Eu3+ was increased by high-pressure application. This behavior was attributed to the distortion of the glass network, which was accompanied with wide variations of bond length and angle. Lochhead and Bray (1995) studied Eu3+ doped sodium disilicate glass with a high-pressure ﬂuorescence line-narrowing technique. This technique was used to characterize the local structure of the Eu3+ ions up to a pressure of 21 GPa. For the crystal-ﬁeld analysis they assumed a C2ν site symmetry which allowed for a complete splitting of the crystal-ﬁeld components. The crystal-ﬁeld strength was determined according to eq. (11). The effect of pressure

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on the 7 F0 → 5 D0 excitation was strongly dependent on the pressure range. From ambient pressure to ∼ 4.7 GPa a red shift of approximately 0.12 nm/GPa was observed. From this pressure up to around 15 GPa the peak position remained unchanged and above 15 GPa a further small red shift was noticed. The bandwidth was constant up to around 7 GPa and increased above that pressure. The interpretation of the high-pressure results presented by Lochhead and Bray (1995) was different for the two characteristic pressure regions below and above 4 GPa. Besides the already mentioned red shift, characteristic features below 4 GPa were an overall crystalﬁeld strength decrease, and a lengthening of the luminescence lifetimes. Lochhead and Bray (1995) explained these results by minor structural changes like simple distortions of the Si– O–Si intertetrahedral angles and a small increase of the overall Eu–O bond covalency. They also noted a possible increase of higher-lying d-state energies relative to those of the f states under pressure. The high-pressure regime from 4 GPa to 21 GPa is characterized by a simultaneous increase of the overall crystal-ﬁeld strength and the 7 F0 → 5 D0 linewidth, along with a shortening of the luminescence lifetimes. In addition, the nearly unchanged 7 F0 → 5 D0 peak position up to 15 GPa suggested that high-ﬁeld Eu3+ sites are created in this pressure range. These high-ﬁeld sites appear on the high-energy side of the 7 F0 → 5 D0 band, which explains the broadening of the band while the peak position remains the same. The application of pressure to silicate glasses results in a gradual coordination change to ﬁve- and six-coordinate species of Si. A proposed mechanism for this coordination increase is through the consumption of nonbridging oxygens. Nonbridging oxygens are covalently bonded to one Si atom (Si–O− ) rather than to two Si atoms (Si–O–Si). In analogy to this process, Lochhead and Bray (1995) argued that a decrease in the nonbridging oxygen concentration should lead to an increase in the Eu3+ site crystal-ﬁeld strength and thus to a blue shift or broadening of the 7 F0 → 5 D0 band. Because of the decreasing concentration, the number of coordinating nonbridging oxygens is decreasing. At the same time, the few remaining nonbridging oxygens are drawn closer to the Eu3+ ions than they would be in the ambient pressure high coordination state to satisfy its overall electrostatic and covalent energy requirements. As the result the high crystal ﬁeld Eu3+ sites are associated with a low local concentration of nonbridging oxygens, low coordination numbers, and short Eu–O bonds. Conversely, weak ﬁeld sites are characterized by a high local concentration of nonbridging oxygens, high coordination numbers, and long Eu–O bonds. These experimental results were completely conﬁrmed by a molecular dynamics simulation by Monteil et al. (2000). 4.6.2. Phase transitions The splitting of free-ion levels by the action of a crystal ﬁeld depends on the symmetry of the crystal ﬁeld which in turn reﬂects the symmetry of the arrangement of the neighboring ions. This property can thus be used to get evidence about the point group symmetry of a site in a given solid once the splitting of the free-ion multiplets have been determined (see, for example, sect. 5.8 of Görller-Walrand and Binnemans (1996)). This can be a very useful

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feature in high-pressure experiments because many materials undergo phase transitions which usually alter the site symmetry. In a stoichiometric compound, the symmetry reﬂected by the splitting is identical with the point symmetry of the site occupied by the rare-earth ion in the solid. However, in the case of rare-earth ions being dopants, the reﬂected symmetry can, but must not, be identical with the point group symmetry of the substituted ion (Denning et al., 1976). This problem arises because the splitting is dominated mainly by the crystal-ﬁeld potential due to the nearest neighbors of the f element (Mishimura and Kushida, 1991). Thus, the splitting mainly reﬂects the symmetry of the arrangement of the ligand ions. Their positions, however, can deviate from the usual positions in the undoped material especially if the rare-earth ion replaces an ion of a distinctly different size. Therefore, the optical site symmetry deduced from the energy level splittings of the doped ion can be different from the real site symmetry of the host. Numerous studies about phases and phase transitions detected by optical investigations of f elements have been published by Haire, Peterson, and co-workers. In many cases they used the Eu3+ ion to correlate the luminescence properties with structural changes. The Eu3+ ion exhibits a variety of characteristic transitions serving as a ﬁngerprint for the structure (Chen et al., 1992e). However, in view of the problematic situation with respect to the local symmetry in the case of doped ions mentioned above, there has been some discussion on whether the Eu3+ ion or f elements in general can be used as indicators of the actual host structure or not (Tanner and Rudowicz, 1993; Stump et al., 1993). In summary, it must be concluded that the spectral/structural correlation has limitations especially in the case of doped ions where deviations between local and real site symmetry may readily occur. To test the feasibility of the Eu3+ ion luminescence method to identify phase transitions, Chen et al. (1992b, 1994b) have performed high-pressure studies on the lanthanide sesquioxide Eu2 O3 under pressure. In this stoichiometric compound the problem of local distortions is ruled out. The lanthanide sesquioxides show only three different crystal structures at ambient conditions, denoted by A, B, and C. The sesquioxides of the larger lanthanide cations tended to be hexagonal (A-type), those of the smallest cubic (C-type), and that of the intermediatesized cations monoclinic (B-type). Some of the sesquioxides, including Eu2 O3 , can exhibit both the B and C structures at ambient conditions. In a high pressure study on C-type Eu2 O3 at room temperature, Chen et al. (1992b) observed distinct changes in the luminescence spectrum of the Eu3+ ion at around 8 GPa. From a comparison with the ambient pressure spectrum of B-type Eu2 O3 , they concluded that the observed changes were due to a phase transition to the B-type monoclinic structure. Such a transition had already been observed by Hoekstra (1966). In a further study, starting with Btype Eu2 O3 , Chen et al. (1994b) observed spectral changes at pressures around 4 GPa. The spectra taken above 4 GPa were found to be similar to the spectrum of the Eu3+ ion in an A-type hexagonal La2 O3 host crystal. Therefore, the observed changes were attributed to a phase transition from B- to A-type structure. Another interesting example is a crystalline to amorphous phase transition in Eu(OH)3 (Chen et al., 1994a) at room temperature. The initial structure is the UCl3 -type structure (space group P 63 /m) which was conﬁrmed by X-ray diffraction. Figure 11 shows that broad bands appear under pressure and completely replace the former sharp lines at around 5.5 GPa. The

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Fig. 11. Luminescence spectra from initially crystalline Eu(OH)3 at different pressures (from Chen et al. (1994a)). Amorphization is observed at 5.5 GPa. The transition is reversible as shown by the spectrum quenched from 11 GPa.

broad bands are characteristic for a sample in an amorphous state (Chen et al., 1995). The transition is completely reversible which can be seen by the spectrum quenched from 11 GPa in ﬁg. 11. As in the case of Eu(OH)3 the UCl3 -type structure can be found in various lanthanide and actinide (lanact) trihalide compounds. Excluding the triﬂuorides, only four different crystal structures can be observed in lanact trihalides. These structures can be ordered according to an increasing M 3+ :X− radius ratio such as: BiI3 -type rhombohedral [6] → AlCl3 -type monoclinic [6] → PuBr3 -type orthorhombic [8] → UCl3 -type hexagonal [9] (Beck and Gladrow, 1979). The numbers in brackets give the respective coordination numbers of the lanact ion. With increasing pressure the radius ratio increases because of the much softer halide ions compared to the metal ions. Thus, according to this increase and the pressure-coordination rule from Neuhaus (1964), it can be expected that high pressure phase transitions should follow the same order. With high pressure X-ray diffraction experiments Beck and Gladrow (1979, 1983) could reproduce a part of this series. In particular, they observed transitions from the AlCl3 -structure and BiI3 -structure to the PuBr3 -structure. Several optical studies, utilizing the f-element luminescence or absorption, could also support phase transitions of lanact trihalides following this sequence: AlCl3 -type → PuBr3 -type: CfBr3 (Peterson et al., 1985, 1987); BiI3 -type → PuBr3 -type: AmI3 (Haire et al., 1985); PuI3 , CmI3 (Haire et al., 1987). Beck and Gladrow (1979) pointed out that a transition from the PuBr3 -structure to the UCl3 -structure can not be realized due to the higher packing efﬁciency ($Vions/Vcell ) in the PuBr3 -structure. Deviating from the above structural series, Wilmarth et al. (1989) reported phase transitions from the UCl3 -structure to the PuBr3 -structure in the case of PrCl3 and PrBr3 , deduced from high pressure absorption and Raman studies. The same transition was observed also in the case of CfCl3 (Peterson et al., 1986; Young et al., 1990) and CmCl3 (Del Cul et al., 1992). In

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principle, such a transition promotes a higher packing efﬁciency, however, it does not ﬁt to the pressure-coordination rule nor to the radius ratio order of the structures. In all cases the phase transitions were proposed because of slight changes in the absorption spectra in connection with Raman spectra. For example, in the case of PrCl3 (UCl3 -structure) above 15.5 GPa a more symmetric shape of the 3 H4 → 1 D2 band and a loss of intensity in and a lack of resolution of the 3 H4 → 1 I6 absorption band in relation to the 3 H4 → 3 P1 absorption band resulted in a spectrum very similar to the orthorhombic PrBr3 (PuBr3 -structure) spectrum. In addition, Raman spectra gave further evidence that a phase transition had occurred around 15 GPa. However, from the very slight changes in the absorption spectra under pressure alone, it seems to be difﬁcult to unambiguously propose an UCl3 to PuBr3 phase transition in these cases. In several optical studies on PrBr3 , NdBr3 , CfBr3 , and CmCl3 a new higher pressure phase beyond the PuBr3 -type structure has been observed (Peterson, 1994). Further studies on LaCl3 :Pr3+ (Gregorian et al., 1989) and La(C2 H5 SO4 )3 ·9H2 O (lanthanum ethylsulfate) doped with Pr3+ (Voloshin and Ivchenko, 1980; Voloshin, 1982), both exhibiting the UCl3 structure at ambient conditions, also revealed phase transitions to a yet unidentiﬁed highpressure structure. The interpretation of this new structure has been tackled in different ways. Gregorian et al. (1989) used the critical ionic radii which mark the stability ranges of the six different lanthanide halide structures (Greis and Petzel, 1974; Beck and Gladrow, 1979). Relating these radii to the structural data obtained under pressure, they found indications of a possible phase transition to the LaF3 -structure at around 10 GPa. This result ﬁtted well to the ﬁrst observation of new unknown lines at around 8 GPa. On the contrary, Voloshin (1988) interpreted the results for LaCl3 :Pr3+ and also for lanthanum ethylsulfate:Pr3+ (Voloshin, 1986) in terms of vibronic states. He argued that the reduction in the distance between f element and its ligands leads to a participation of the f orbitals in the chemical bond. This would cause a vanishing of the pure electronic transitions and the appearance of vibronic lines. In the general case the symmetry should be lowered and all degeneration should be lifted. In summary, these examples clearly show that the luminescence spectra of the f elements deﬁnitely have the ability to indicate a phase transition, however, unambiguous conclusions about the structure of the new phases are quite difﬁcult to draw and may be restricted to special cases. 5. Intensities and lifetimes of f-f transitions 5.1. General considerations Most electronic transitions between different states of the f-electrons are dominated by electric dipole transitions. Only in exceptional cases like Eu(III), magnetic dipole transitions are found to be as strong as electric dipole transitions. However, in the case of an f element, electric-dipole transitions between the 4fN states are forbidden because the parity of initial and ﬁnal state is conserved. Only when the f element is embedded in a crystal providing a point group symmetry that does not contain the inversion operation, these transitions can be observed readily. In an actual experiment, two different physical quantities connected with electric (or magnetic) dipole transitions are accessible via optical studies, on the one hand the intensities of the

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transitions and on the other hand the lifetimes of the excited levels. For transitions between different J multiplets, where the crystal-ﬁeld split levels of the initial multiplet are equally occupied, the experimental quantities can be easily related to the oscillator strengths used in the parameter calculations. In the case of absorption spectroscopy the integrated area of a transition peak I0 can be compared directly to the experimental oscillator strength P according to (Görller-Walrand and Binnemans, 1998): 8π 3 NA 1 (n2 + 2)2 1 I0 = ν0 DED + DMD · n and hc 2303 3 9n 2J + 1 8π 2 me cν0 1 me c 2 (n2 + 2)2 1 P= (17) D + D = 2303 · n I0 , ED MD he2 3 9n 2J + 1 πNAe2 where h is Planck’s constant, c the speed of light, NA Avogadro’s constant, ν0 the wavenumber at the absorption maximum, n the refractive index of the material, J the total angular momentum of the ground multiplet, me the electron mass, e the elementary charge, and D the dipole strength in a randomly oriented system. The dipole strength can be calculated from the # (MD or ED operator): matrix element of the dipole operator O 2 D = %i # (18) O%f . In the case of luminescence transitions it is usually not appropriate to use the absolute intensities because non-radiative processes such as multiphonon decay or energy transfer processes can effectively change the observed intensities. Similarly, also the experimentally measured lifetime is not suitable because non-radiative processes can effectively shorten the lifetime. However, the radiative branching ratios βR can still be compared with the calculations. These ratios denote the relative intensities for transitions from the same initial to different ﬁnal multiplets. Only if non-radiative processes can be discarded, as for example in cases of diluted f elements with multiplets lying well above the next lowest levels, the radiative lifetimes τR can be compared with theoretical calculations. In this case the radiative lifetime is inversely proportional to the oscillator strength of the transition. The remaining problem in the calculation of intensities and radiative lifetimes is the calculation of the dipole or, in other words, the oscillator strength matrix element in eq. (18). To calculate this element, Judd (1962) and Ofelt (1962) proposed the transition oscillator strengths being due to the mixing of the 4fN−1 nd1 and 4fN−1 ng1 conﬁgurations into the 4fN conﬁguration by the crystal ﬁeld. Because this mixing introduces components of different parities, the transitions become allowed. Although this theory has been widely and successfully employed to describe the total oscillator strengths of transitions between different J multiplets, it has been pointed out that also other mechanisms as for example mixing with ligand states will contribute to the observed oscillator strengths (Poon and Newman, 1984). In the scope of the Judd–Ofelt theory three parameters Ω2 , Ω4 , and Ω6 are commonly used to describe the transitions between J multiplets. For this case, the contributions from individual crystal ﬁeld split levels of a given multiplet are simply summed up. To account for individual transitions, effective transition operators can be used to derive a parametrization

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analogous to the crystal-ﬁeld Hamiltonian. This procedure introduces parameters Aλtp , which can be used to calculate the Judd–Ofelt parameters. For a detailed account of this subject see, for example, Görller-Walrand and Binnemans (1998) and Reid (2000). As discussed, intensities and lifetimes are related to the oscillator strengths of the f-f transitions which in turn are connected to the mixing of excited conﬁgurations 4fN−1 nd1 , 4fN−1 ng1 or ligand states to the 4fN conﬁguration. The mixing results from conﬁguration interactions due to the odd-parity crystal-ﬁeld components in the ﬁrst case and overlap and covalency contributions in the second case. These considerations form the starting-point of high-pressure experiments. The application of high pressure to f-element compounds should change the conﬁguration interaction as well as the interactions with the ligands. Thus, both intensities and lifetimes should be inﬂuenced by pressure. The direction and magnitude of this inﬂuence, however, is difﬁcult to forecast because pressure will act in different ways. The mixture with excited conﬁgurations is determined by the energy difference and the size of the matrix elements of the crystal-ﬁeld potential between the conﬁgurations. Obviously, the intensity of a transition depends on the amount of this mixing which can be increased (decreased) by decreasing (increasing) the energy difference to the excited conﬁgurations or increasing (decreasing) odd-parity components of the crystal-ﬁeld potential. Overlap and covalency contributions can be expected to increase under pressure, leading to enhanced mixing and oscillator strengths. However, the increased interaction with the ligands may also lead to enhanced non-radiative decay in case of luminescence measurements, which then would diminish the intensities and lifetimes. It should be noted that also the refractive index in eq. (17) will change under pressure. This change can be estimated by the Lorenz local-ﬁeld model, where the refractive index n is related to the atomic polarizability αP and the density of the material ρ by the Lorentz–Lorenz relation: n2 − 1 4πNA (19) = αP ρ. n2 + 1 3 According to eq. (19) the refractive index increases with increasing density (increasing pressure) and increasing polarizability. However, this model is exactly valid only for point dipoles in a cubic arrangement. Therefore, the reliability of this model with respect to quantitative predictions is limited in many cases (Eremets, 1996). A further difﬁculty here is to estimate the change of the polarizability under pressure. Johannsen (1997) performed high-pressure experiments on alkali halides to determine the changes of the refractive index with increasing density. According to his results, an increase of the density by around 20% causes an increase of the refractive index of less than 3%. Such a change would increase the intensity of a transition by less than 10% and can thus explain only slight changes in the intensities. In the following sections it will be shown that a careful analysis of the high pressure effects on intensities and lifetimes can yield valuable information about various aspects of physical interactions leading to the observed intensities and lifetimes. At ﬁrst, absorption studies will be presented which have the advantage that the observed intensities can be related di-

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rectly to the oscillator strengths. In the subsequent section luminescence studies will be discussed where it is possible to study effects due to conﬁguration interactions or energy transfer processes. 5.2. Absorption studies Only a few absorption studies under pressure with respect to the intensities of f-f transitions can be found in the literature. A systematic and comprehensive study of rare-earth ions in ionic crystals has been performed by Keating and Drickamer (1961a). They studied rare-earth trichlorides, triﬂuorides, and ethylsulfates at room temperature up to pressures of 18 GPa by means of absorption spectroscopy. The rare earths studied were Pr3+ , Nd3+ , Sm3+ , Ho3+ , Er3+ , and Tm3+ . In all cases they observed an increase of the intensities by approximately 40%. To explain this result, they assumed the crystal-ﬁeld potential arising from point charges only. In this case the potential contains odd-parity terms proportional to Ri−4 , Ri−5 , and Ri−6 , where Ri is the distance between the nucleus of the rare-earth ion and the charge ei of a ligand ion. Estimating a volume reduction of 15–20% at 10 GPa and taking into account only the most important Ri−4 term, Keating and Drickamer (1961a) could obtain a theoretical intensity increase of about 45%, in good agreement with the experimentally determined increase. Therefore, they concluded that the increase in intensity was due to an increased mixing of 5d and 4f orbitals due to an increase of the mixing potential. To extend these studies, Keating and Drickamer (1961b) also investigated UF3 and UF4 . In the case of UF3 the results were similar to the rare-earth ﬂuorides, in particular an increase in intensity could be observed for all transitions. However, for UF4 they observed increasing as well as decreasing intensities for different lines under pressure. The U4+ ion in UF4 is situated in a position which is only slightly distorted from having a center of symmetry. Thus, the oddparity components of the crystal-ﬁeld potential can be quite small and one has to search for other mechanisms contributing to the intensities which can cause the observed decrease under pressure. One mechanism is the mixing of f- and d-orbitals by lattice vibrations. According to Keating and Drickamer (1961b) the mixing is proportional to (r0 /r)2 Ve , where Ve is the even part of the crystalline potential, r0 denotes the amplitude of vibration of the metal nucleus, and r is the radius of the f orbital. The intensity is proportional to the square of this quantity. Under pressure, Ve and r can be expected to increase, whereas r0 can be assumed to decrease. In total, this quantity may therefore increase or decrease, depending on the size of the various contributions. Because at the same time the mixing via the odd-parity components of the crystal ﬁeld can be quite small, it may easily occur that some of the intensities, which are dominated by the lattice vibration mixing show a decreasing intensity under pressure. 5.3. Luminescence studies In luminescence studies it can often be observed that intensities decrease with increasing pressure. A decreasing luminescence intensity can be ascribed to two main effects. On one hand, the excitation efﬁciency can decrease due to a pressure-induced shift of absorption bands away from a ﬁxed excitation energy. This effect can be minimized either by a tunable excitation source or by exciting into a band, whose shift is negligible compared to its width.

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On the other hand, the luminescence quantum efﬁciency can decrease. Apart from a decrease of the oscillator strengths themselves, many other mechanisms can cause such reduced quantum efﬁciencies, as, for example, enhanced electron–phonon coupling, generation of new paths for deexcitation or energy transfer processes. In fact, these processes will not affect the oscillator strengths of the transition but simply inﬂuence the occupation of the excited level. Therefore, the oscillator strength of a given transition may still increase under pressure, however, this increase is completely covered up by a fast depletion of the excited level. The lifetime of an excited level can be used here to distinguish between a change in the oscillator strength or the occupation of an excited level. A decreasing oscillator strength is connected with an increasing lifetime and vice versa. Thus, if the lifetime of a level is decreasing under pressure, the intensity must increase. However, if on the contrary a decreasing intensity is observed, some depletion process must be present and dominate a possible increase in the oscillator strength. Besides depletion also ﬁlling processes may occur under pressure. Such a process would require some long-living reservoir which slowly ﬁlls the excited level. As a result, a strong enhancement of the intensity may be observed, independent of a change in the oscillator strengths. The measurement of a lifetime is much more accurate and reliable than the measurement of the absolute luminescence intensity under pressure. Therefore, the majority of studies on f-element compounds reported on pressure-dependent lifetimes only. The compounds studied so far can be found in table 1. In most cases a decrease of the lifetime under pressure has been observed. The following sections will treat the changes in lifetimes or intensities according to the mechanisms responsible for the observed variations. 5.3.1. Inﬂuence of 4f N−1 5d1 conﬁgurations Excited 4fN−1 5d1 conﬁgurations can inﬂuence the f-f transitions in two different ways: ﬁrst, a thermal excitation from excited 4fN states to the 4fN−1 5d1 conﬁguration can lead to a quenching of the f-f luminescence and decreasing lifetimes, and second, an increased (decreased) mixing of 4fN−1 5d1 to the 4fN wavefunctions can cause increasing (decreasing) intensities and decreasing (increasing) lifetimes. One of the best studied systems is SrFCl doped with Sm2+ . Jovani´c et al. (1997a) studied the lifetime of the 5 D0 → 7 F0 transition of the Sm2+ ion as a function of pressure and found a pronounced exponential decrease from approximately 1.4 ms to 0.5 ms up to 10 GPa. In a subsequent paper they used the Lorentz–Lorentz equation (eq. (9)) to attribute the observed decrease of the lifetime to changes of the refractive index under pressure (Jovani´c et al., 1997b). The same explanation was also applied to the case of the mixed crystal SrFCl0.5 Br0.5 :Sm2+ , where a similar decrease of the lifetime was noted (Jovani´c, 2001). Although in both cases a good agreement between calculated and experimental values was reached, the model used is clearly oversimpliﬁed. Despite many assumptions on polarizabilities, dipole matrix elements and others, Jovani´c et al. (1997b) neglected all other radiative transitions from 5 D0 . Taking into account these transitions, which contribute to the overall transition probability and henceforth to the lifetime, one would have to consider for example different factors for the energies, the wavelength dependence of the refractive index, and a completely different factor for the magnetic dipole transition 5 D0 → 7 F1 (see eq. (17)).

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In addition, from structural data for SrFCl (Shen et al., 1994) under pressure, the increase of the density of SrFCl up to 10 GPa can be calculated to be approximately 13%. Comparing this increase with the high-pressure experiments on the refractive index of the alkali halides (Johannsen, 1997), one can expect a small change of perhaps 2% of the refractive index. Such a change should decrease the lifetime by no more than a few percent. Nevertheless, the studies from Jovani´c and coworkers at least indicate that the change of the refractive index under pressure may give rise to some corrections of quantitative evaluations of pressure effects. The lowest state of the 4f55d1 conﬁguration of SrFCl:Sm2+ is located only at around 19 000 cm−1 above the 7 F0 ground state of the 4f6 conﬁguration (Shen and Bray, 1998a). Under pressure, the energy distance between both conﬁgurations is rapidly decreasing. This should provide a unique possibility to study the inﬂuence of this conﬁguration on intensities and lifetimes of the f-f transitions. Following these considerations, Shen et al. (1997) and Shen and Bray (1998a, 1999) have presented a detailed investigation on SrFCl:Sm2+ and CaFCl:Sm2+ . They considered two effects, on one hand the mixing of the wavefunctions of the 4f6 and 5 4f 5d1 conﬁgurations and on the other hand the nonradiative crossover between levels of both conﬁgurations. To analyze the nonradiative crossover, they used the single conﬁgurational coordinate (SCC) energy level diagram for Sm2+ in SrFCl depicted in ﬁg. 12. The missing 7 FJ (J = 0, . . . , 6) multiplets would be placed directly below the 5 DJ (J = 0, . . . , 2) multiplets with the minimum of the 7 F0 parabola at the zero of energy. The 5 DJ (J = 0, . . . , 2) multiplets have small Franck–Condon offsets relative to the ground 7 F0 multiplet, in contrast to the much larger Franck–Condon offset for the excited 4f5 5d1 conﬁguration.

Fig. 12. Single conﬁgurational coordinate energy level diagram for SrFCl:Sm2+ (from Shen and Bray (1998a)). For details see text.

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The quantities used in ﬁg. 12 are the energies E relative to the ground state 7 F0 , the energy differences phω ¯ between different states, where h¯ ω is the energy of the single optical phonon associated with the diagram and p is the number of phonons bridging the respective energy gaps, the populations N , and radiative W r and nonradiative W nr transition rates. All quantities are characterized by indices d, J or J or combinations thereof, where d denotes the 4f5 5d1 conﬁguration and J , J different 5 DJ multiplets. Studying the intensities and lifetimes as a function of temperature ﬁrst, Shen and Bray (1998a) could ﬁt the radiative and nonradiative rates depicted in ﬁg. 12 to the experimentally observed variations. They obtained excellent agreement of calculated and experimental results. In particular, it was shown that quenching of the 5 D2 luminescence with increasing temperature between 50 K and 100 K is due to a thermally induced 5 D2 → 4f5 5d1 → 5 D1,0 crossover. Further quenching of the 5 D1 luminescence at temperatures above 100 K, could be assigned to a thermally induced 5 D1 → 4f5 5d1 → 5 D0 process and a direct 5 D1 → 5 D0 multiphonon relaxation process. In a second step, Shen and Bray (1998a) studied the changes of the 5 D0 and 5 D1 lifetimes of SrFCl:Sm2+ and CaFCl:Sm2+ under pressure. In both systems they observed an exponential decrease as shown in ﬁg. 13 for the case of the 5 D0 lifetime at room temperature. According to their analysis of the temperature effects, the measured lifetime of the 5 D0 → 7 F0 transition represents an almost pure radiative lifetime. A strong decrease under pressure therefore indicates an increase in the radiative rate WJr . This in turn was attributed to an increased elec-

Fig. 13. Calculated and experimental results for the pressure dependence of the RT 5 D0 lifetimes of SrFCl:Sm2+ and CaFCl:Sm2+ (from Shen and Bray (1998a)). The data for CaFCl:Sm2+ are shifted with respect to those of SrFCl:Sm2+ by a pressure of 2.2 GPa. The solid and dashed curves were calculated as explained in the text.

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tronic 4f5 5d1 admixture resulting from a shift of the 4f55d1 conﬁguration to lower energy with pressure. To study this admixture in detail, Shen and Bray (1998a) calculated the radiative rates taking into account electric and magnetic dipole transitions. While magnetic dipole transitions are allowed within the 4f shell, electric dipole transitions depend on the size of the wavefunction mixing due to odd crystal-ﬁeld terms. In their calculation, Shen and Bray (1998a) considered the conventional Judd–Ofelt electric dipole contribution, designated as the 2nd electric dipole contribution, as well as a 3rd electric dipole contribution suggested by Wybourne (1968). This contribution takes into account the spin–orbit coupling of multiplets with different spin states in the excited conﬁguration. This coupling, in connection with the odd crystal-ﬁeld terms, is capable of mixing different spin states to the multiplets of the 4f6 conﬁguration, thus relaxing the spin selection rule for the 5 D0 → 7 F0 transition. Only three quantities, two odd crystal-ﬁeld parameters B01 and B03 and the energy distance Ed between the two conﬁgurations, were used as parameters in the calculations to describe the changes of the 5 D0 lifetime. Performing the ﬁts, Shen and Bray (1998a) assumed a linear dependence of B01 , B03 /B01 , and Ed on pressure. As the result for the pressure dependence of these quantities they ﬁnally found (p in GPa, Ed and B0k in cm−1 ): Ed = 18630 − 230(2)p, 1010B01 = 56(2) + 6.4(6)p, B03 /B01 = 104(8) − 7.0(8)p.

(20)

The calculated lifetimes, taking into account these shifts, are included in ﬁg. 13 as dashed and solid lines. They show an excellent agreement with the experimental values. The pressure shift of −230 cm−1 /GPa of the excited 4f5 5d1 conﬁguration, deduced from the lifetime calculations, also agrees well with the experimental value of −200 cm−1 /GPa for pure SmFCl given by Bolduan et al. (1985). This gives strong evidence that taking into account magnetic and the two electric dipole contributions is necessary to completely describe the behavior of the 5 D0 lifetime. In particular, this result shows that the spin–orbit coupling within the excited conﬁguration gives an important contribution for the mixing of the wavefunctions via the odd crystal-ﬁeld parameters. More difﬁculties arose in the case of the calculated 5 D1 lifetime under pressure, which showed only poor agreement with experiment. The reasons for this disagreement were not understood, but were tentatively related to a breakdown of the closure approximation used in the model. Gleason et al. (1993) presented a study on La2 O2 S:Tb3+ and Gd2 O2 S:Tb3+ under pressure. Tb3+ has a similar energy level structure to Sm2+ , the main difference is a reversed order of the multiplets with respect to the total angular momentum J . Accordingly, the ground state is 7 F6 and the multiplet with the highest energy of the 7 F term is 7 F0 , located at approximately 6000 cm−1 above the ground state. The next highest multiplets are 5 D4 and 5 D3 , at around 20000 cm−1 and 26500 cm−1 , respectively. The 4f7 5d1 conﬁguration lies only about 2000 cm−1 above the 5 D3 multiplet. Under pressure, Gleason et al. (1993) observed a strong decrease of the 5 D3 lifetime, which was attributed to a nonradiative transfer to the excited 4f7 5d1 conﬁguration. This conﬁguration

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was shown to rapidly shift with a rate of −460 cm−1 /GPa to lower energies. Considering the nonradiative transfer in the SCC model, they could successfully describe the pressure-induced variation of the lifetime of the 5 D3 multiplet. The lifetime of the lower-lying, isolated 5 D4 multiplet of Tb3+ should be determined mainly by radiative transitions, similar to the case of the 5 D0 multiplet of Sm2+ . However, in the case of Tb3+ no change of the lifetime and hence of the radiative rate, was observed under pressures up to 5 GPa. This indicates that the mixing with the excited 4f7 5d1 conﬁguration does not change, despite of the large shift with pressure. One reason may simply be that the energy difference between the 5 D4 multiplet and the 4f7 5d1 conﬁguration for Tb3+ is larger at ambient pressure than in the case of SrFCl:Sm2+ . However, due to the strong shift, this difference becomes comparable to Sm2+ at around 5 GPa. Thus, a change of the lifetime should have been observed in this pressure range. The obvious differences may indicate for example a different variation of the odd crystal-ﬁeld parameters for La2 O2 S:Tb3+ . Another possibility is that the spin–orbit coupling contribution, which was very important for the change in the lifetime of 5 D0 of Sm2+ , does not play any signiﬁcant role in the case of the 5 D4 multiplet of Tb3+ . This could mean that the spin–orbit coupling contribution is not important either speciﬁcally for the 5 D4 multiplet or for Tb3+ in general. 5.3.2. Inﬂuence of charge transfer states Similar to the inﬂuence of the excited 4fN−1 5d1 conﬁgurations, charge transfer states (CTS) can affect the lifetimes and intensities of f-f transitions in two different ways. On one hand the possibility for nonradiative energy transfer from an excited level of the 4fN conﬁguration to the CTS is enabled and on the other hand the wavefunctions of the CTS can be mixed to the 4fN conﬁguration. The lifetimes of the f-f transitions should decrease with increasing nonradiative energy transfer or increasing wavefunction mixing. Furthermore, the intensities should decrease with increasing nonradiative transfer but increase with enhanced wavefunction mixing. A system which has been studied in some detail under pressure is R2 O2 S:Eu3+ (R = Y, La). The conﬁgurational coordinate diagram of Y2 O2 S:Eu3+ is shown in ﬁg. 14. In many regards the energy level scheme is similar to the isoelectronic Sm2+ in SrFCl (see sect. 5.3.1). The main difference is that the ﬁrst excited state is not an intrinsic ionic state of the rareearth ion itself, but an extended state involving the wavefunctions of the ligand orbitals. It is therefore interesting to look for possible differences in the high pressure behavior. A detailed analysis of this system at ambient pressure has been performed by Fonger and Struck (1970) and Struck and Fonger (1970). They studied the intensities and lifetimes of the 5 D multiplets as a function of temperature and attributed the observed changes to thermally J promoted transitions 5 D → CTS followed by return crossovers to lower 5 D states. Such a process is indicated by arrows in ﬁg. 14. On the contrary, Wickersheim et al. (1968) have reported similar measurements, but tried to explain the successive quenching of the 5 D states through multiphonon emission. To get further evidence about which model is more appropriate, Webster and Drickamer (1980a) have measured the luminescence efﬁciency of La2 O2 S:Eu3+ and Y2 O2 S:Eu3+ and the lifetimes of the lanthanum compound under pressures up to 12 GPa. Intensities and life-

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Fig. 14. Conﬁgurational coordinate diagram for La2 O2 S:Eu3+ showing the position of the charge transfer state (CTS) at ambient and high pressure (from Webster and Drickamer (1980a)). The arrows indicate the 5 DJ → CTS → 5 DJ (J > J ) relaxation pathway. (10 kbar = 1 GPa).

times of La2 O2 S:Eu3+ and Y2 O2 S:Eu3+ were also measured by Gleason et al. (1993) and Wang et al. (1984), respectively, who got mainly the same results as Webster and Drickamer (1980a). To exclude effects due to energy transfer between different Eu3+ ions, Webster and Drickamer (1980a) their discussion on the results for the sample with the lowest Eu3+ concentration of 0.1%. For higher concentrations up to 3% they could prove that a damping of the pressure effects occurred, however, the basic ﬁndings were the same. To explain the high-pressure results, Webster and Drickamer (1980a) slightly modiﬁed the model from Struck and Fonger (1970). They took into account an activation energy Ei act , related to the energy difference between the 5 Di level and the CTS, and various nonradiative processes. To determine the crucial position of the CTS under pressure, Webster and Drickamer (1980a) performed absorption studies and found a blue shift of the CTS at a rate of approximately 180 cm−1 /GPa. The position of the CTS at 12 GPa is shown in ﬁg. 14. Taking into account this large shift, the 5 D → CTS → 5 D high-pressure model predicts distinct changes of the 5 DJ lifetimes and intensities. Actually, the main effects on the intensities of the 5 DJ → 7 F0 (J = 0, 1, 2, 3) transitions of La2 O2 S:Eu3+ under pressure are found to perfectly match with the 5 D → CTS → 5 D model. In particular, Webster and Drickamer (1980a) found that the emissions from 5 D0 and 5 D1 decreased in intensity with increasing pressure. On the contrary, the very weak 5 D2 emission increased by a large factor, stayed approximately constant between 2 GPa and 8 GPa and ﬁnally decreased above 8 GPa. The emission of 5 D3 appeared at about 5–6 GPa and increased rapidly in intensity. The results for Y2 O2 S:Eu3+ differed quantitatively from the results for La2 O2 S:Eu3+ , but this could be explained simply by the difference in location of the charge transfer state and

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its shift with pressure. Finally, it should be noted that the changes in the lifetimes of the 5 DJ multiplets could also be described with the above model. The high-pressure results therefore clearly support the model of luminescence quenching due to a 5 D → CTS → 5 D crossover in favor of nonradiative decay. Further systems in which the nonradiative energy transfer from ligand states to f elements has been studied in detail are the [Pt(CN)4 ]3 and [Au(CN)2]3 complexes. In particular, Yersin and coworkers have studied Eu2 [Pt(CN)4 ]3 ·18H2 O (Yersin et al., 1979), Sm2 [Pt(CN)4 ]3 ·18H2 O (Yersin and Stock, 1982), and Eu[Au(CN)2]3 ·3H2 O (Yersin et al., 1998). These systems are of great interest to energy transfer investigations since they exhibit extraordinary properties which mainly result from the unusual arrangement of the [Pt(CN)4 ]2− 3 and [Au(CN)2 ]3 complexes, acting as donors. In the case of R2 [Pt(CN)4 ]3 ·18H2O, the [Pt(CN)4 ]3 complexes are arranged in linear stacks, leading to highly coupled electronic wavefunctions along the stacking axis (c-axis). The rare-earth ions are the acceptors located between the stacks. The [Au(CN)2]3 complexes in Eu[Au(CN)2]3 ·3H2 O form two-dimensional layers alternating with layers of rare-earth ions. The low-energy states of the dicyanoaurates(I) as well as the tetracyanoplatinates(II) can be traced to the Au (Pt) 5d, 6s HOMO and the Au (Pt) 6p, CN π ∗ LUMO, respectively (Yersin and Gliemann, 1978). Due to the strong electronic interaction between the complexes, valence and conduction bands develop. Finally, strong electron–hole interactions lead to excitonic states with a binding energy of up to 4000 cm−1 (Eichhorn et al., 1981). One of the outstanding properties of these substances is the extreme tunability of the electronic states under high pressure. In many cases a red shift on the order of 2000 cm−1 /GPa has been observed (Yersin and Riedl, 1995). In addition, an effective nonradiative energy transfer from the cyano donor complexes to the f elements has been observed. In the case of Eu[Au(CN)2]3 ·3H2 O this process even totally quenches the otherwise very intense and broad emission from the [Au(CN)2 ]− layers. However, because of the very strong red shift of the donor electronic states, it is possible to shift the donor states over different levels of the f element. Especially, resonant and nonresonant energy transfer conditions can be achieved to study the transfer mechanism. Figure 15 shows the emission spectra of single crystal Eu[Au(CN)2]3 ·3H2 O at various pressures (Yersin et al., 1998). At ambient pressure only luminescence from the Eu3+ ion (5 D0 → 7 FJ and some weak transitions from 5 D1 ) but no luminescence from the donor can be observed. However, at pressures above approximately 1 GPa at 20 K, a very weak emission occurs and grows in with increasing pressure. This effect is a consequence of a pressureinduced tuning off of the nonradiative energy transfer from the dicyanoaurate(I) donors to the Eu3+ acceptors. Taking into account the pressure dependence of the donor emission band, it is possible to extrapolate the ambient pressure position to be about 23600 ± 300 cm−1 . The transfer rate PD−A between donor D and acceptor A can be expressed by (Förster, 1951; Dexter, 1953): PD−A = F (R) fDe (¯ν )fAa (¯ν ) d ν¯ . (21)

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Fig. 15. Luminescence spectra of single-crystal Eu[Au(CN)2 ]3 ·3H2 O at various pressures (T = 20 K, λexc = 363.8 nm). With increasing pressure, the energy transfer from the dicynoaurates donors to the Eu3+ acceptors can successively be tuned off. The vertical lines characterize positions of Eu3+ absorptions and emissions, respectively (from Yersin et al. (1998)). (10 kbar = 1 GPa).

The integral is the spectral overlap integral of the donor emission fDe (¯ν ) with the acceptor absorption proﬁle fAa (¯ν ) for resonance condition. F (R) summarizes the essential mechanisms, like the Dexter (1953) exchange or the Förster (1951) multipole mechanism with their speciﬁc R distance dependences.

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According to eq. (21), resonance energy transfer can occur only if the spectral overlap integral differs from zero. At ambient pressure, this is the case for only two multiplets of Eu3+ , 5 L and 5 D , with estimated barycenters near 25100 cm−1 and 24300 cm−1 , respectively. 6 3 With increasing pressure, the spectral overlap integral with these multiplets is tuned to zero, leading to the appearance of the donor emission. With further increasing pressure, the overlap integral is continuously tuned on and subsequently off with the lower lying multiplets of Eu3+ in the order 5 D2 (maximum overlap at around 1.6 GPa), 5 D1 (3.9 GPa) and 5 D0 (5.3 GPa). At 1.6 GPa the intensity of the donor emission increased by a factor of 10, although the spectral overlap with 5 D2 reached its maximum. This clearly reveals that the energy transfer is much more efﬁcient to 5 D3 than to 5 D2 . At the highest pressures the overlap is zero with all but the lowest 5 D0 multiplet. Under these conditions no f-f luminescence could be observed at all, showing that no energy transfer from the donor to the 5 D0 multiplet occurs. Similar examples for energy transfer from ligand localized levels to highly localized 4f levels are represented by the rare-earth chelates. Voloshin and Savutskii (1976) studied europium benzoylacetonate under pressures up to 6 GPa. Exciting the triplet level they could observe the luminescence from the Eu3+ ion. It was possible to describe the observed initial increase in the quantum yield of the Eu3+ luminescence up to 2.5 GPa and the following decrease by the exchange resonance theory (Dexter, 1953). A more detailed study on different Tris chelates of Sm3+ , Eu3+ , Gd3+ , and Tb3+ with β-diketonates was performed by Hayes and Drickamer (1982), where the most dramatic effects of pressure on energy transfer phenomena were found for the Eu3+ chelates. A schematic diagram of the ligand localized and Eu3+ excited energy levels are shown in ﬁg. 16. The ligand levels are denoted with S and T for the singlet and triplet states, respec-

Fig. 16. Energy transfer processes in Eu chelates (from Hayes and Drickamer (1982)). Wiggly arrows represent nonradiative processes. Solid and dashed arrows represent radiative processes, with a lesser probability for the dashed arrows; a, b, c, d: see text.

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tively. Under pressure both levels show a strong red shift. The shift of the lower-lying triplet levels was 1400 cm−1 for Thenoyltriﬂuoroacetylacetone (TTF) and 1000 cm−1 for Dibenzoylmethide (DBM) up to 4 GPa. The simultaneous shift of the 5 DJ multiplets of Eu3+ is more than one order of magnitude smaller. Figure 16 also indicates the various optical processes that were observed in europium chelates in the study of Hayes and Drickamer (1982). Part (a) illustrates the excitation of the singlet ligand state, followed by a relaxation to the triplet state and a subsequent energy transfer process which induces the emission of the Eu3+ ion. Part (c) shows the situation at higher pressures, when the triplet level lies between 5 D1 and 5 D0 . In this case a relaxation from the excited 5 D1 to the 5 D0 multiplet can occur via the intermediate triplet level under proper conditions. Finally, part (b) and (d) indicate a thermal deactivation process back to the ligand localized levels. This process already occurs with the triplet level above 5 D0 (see part d) and is responsible for a pronounced quenching of the 5 D0 luminescence at higher pressures for EuDBM. One of the aims of the high pressure studies of Hayes and Drickamer (1982) was to test this triplet quenching hypothesis (Sato and Wada, 1970). According to part (d) of ﬁg. 16, an activation energy EA is needed to transfer the energy stored in 5 D0 to the triplet level. This energy can be slightly larger than the energy difference E between 5 D0 and the triplet level (Struck and Fonger, 1975). Assuming that the quenching of the 5 D0 luminescence in EuDBM can be related with this process, a one-to-one correspondence of the red shift of the triplet energy and the change in the activation energy should be found. Under pressure exactly this behavior was found, which deﬁnitely conﬁrmed the triplet quenching process as the main mode of thermal deactivation in these systems. 5.3.3. Energy transfer processes in insulators In the preceding section the pressure effects on the energy transfer from electronic states of constituents of the host lattice to the f element have been discussed. Different to this case, another source of energy transfer can be the electronic state of some point defect in the host lattice which will be considered now. As simple examples, the point defect can be another f element (either of the same or a different kind) or a transition metal element. Pressure effects on the energy transfer between f elements of the same kind were studied by Merkle et al. (1981) for the case of Nd3+ –Nd3+ pairs in Ndx Y1−x P5 O14 (x = 1, 0.1). This material was studied in detail because of its potential use as a stoichiometric laser material. An outstanding property is a very weak concentration quenching of the luminescence. The total luminescence decay rate of the 4 F3/2 multiplet in Ndx Y1−x P5 O14 (x = 1, 0.1) under pressure is shown in ﬁg. 17. Obviously the stoichiometric compound shows a much larger increase of the decay rate than the doped compound. Merkle et al. (1981) discussed three possible mechanisms of the pressure-enhanced decay rate: an increase of the radiative decay rate of each Nd3+ ion, an increase of the nonradiative decay rate of each Nd3+ ion, or an increase in the interaction between Nd3+ ions leading to luminescence quenching. The nonradiative decay rates for the 4 F3/2 multiplet were estimated to contribute less than 20% to the total decay rate (Powell et al., 1980) at ambient pressure.

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Fig. 17. Total luminescence decay rate of 4 F3/2 in Ndx Y1−x P5 O14 for x = 0.1 and 1.0, as a function of pressure (from Merkle et al. (1981)).

Because it is very unlikely that pressure can cause an increase of this small contribution to the extent necessary to explain the NdP5 O14 data, the second possibility was ruled out. The increase in the radiative decay rate of 4 F3/2 under pressure was estimated from the measured absorption strength of the 4 I9/2 → 4 F3/2 transitions and the relative luminescence intensities for NdP5 O14 . It was found that an increase by a factor of about 1.2(4) can be expected. However, this value is much smaller than the observed increase (see ﬁg. 17) and thus cannot be used to explain the experimental results. Because it has been shown that the oscillator strengths for Nd3+ transitions in Ndx La1−x P5 O14 are independent of the Nd3+ concentration (Auzel, 1976), it can be assumed that the change in the radiative decay rate with pressure should also depend little on concentration. Therefore, the same estimated increase of 1.2(4) for the stoichiometric compound can be expected also in the case of the doped sample. Indeed, in this case the experimental result agrees well with the prediction. This clearly reveals that in the case of the stoichiometric compound a further mechanism, which is not due to single-ion processes, must contribute to the increased decay rates. Merkle et al. (1981) considered two multi-ion quenching processes that are possible in this case, namely a cross-relaxation between pairs of Nd3+ ions and energy migration to sinks. A possible strong increase of the cross-relaxation mechanism Nd(4 F3/2 ) + Nd(4 I9/2 ) → Nd(4 I15/2) + Nd(4 I15/2) could be ruled out because of various spectral properties observed under pressure. The ﬁnal possibility therefore was an increased energy migration to traps. To check the plausibility of this hypothesis, Merkle et al. (1981) used a simple diffusion model, where the rate of energy transfer to traps is proportional to the energy diffusion coefﬁcient, D, which can be calculated for resonant dipole–dipole interaction by (Trlifaj, 1958): −1 2 νhom . W mig ∝ D ∝ a −4 Wion

(22)

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Here the average lattice spacing is denoted by a, Wion is the single-ion transition rate and νhom is the homogeneous linewidth which is used to approximate the spectral overlap integral between the two interacting ions. As the result, the decay rate due to migration should increase by a factor of 2.4(1.0) up to 6.8 GPa. Correcting the data from ﬁg. 17 for the change of the radiative decay rate one ﬁnds an experimental increase by a factor of 2.2(3). This value is in close agreement with the prediction from eq. (22). Therefore, Merkle et al. (1981) concluded that energy migration is the dominant effect leading to an increase in the decay rates of NdP5 O14 under pressure. Similar conclusions were drawn by Blanzat et al. (1984) who studied Tbx La1−x P5 O14 , Eux La1−x P5 O14 and mixed single crystals Tbx Eu1−x P5 O14 under pressure. By selective excitation of the 5 D4 multiplet of Tb3+ the luminescence of Eu3+ could be observed due to an efﬁcient Tb3+ → Eu3+ energy transfer. Under pressure the lifetime of the Eu3+ luminescence decreased which was interpreted by a weak back-transfer from Eu3+ to Tb3+ due to the increased overlapping of the 5 D4 multiplet of Tb3+ with the 5 D2 multiplet of Eu3+ . The decay of the Tb3+ luminescence in the mixed crystals is dominated by a very fast energy diffusion process to the Eu3+ acceptors at ambient pressure, leading to a singleexponential decay. The decay time increases with increasing Tb3+ concentration which is characteristic for a diffusion-limited relaxation mechanism since the average distance required for energy to migrate to an Eu3+ ion is increased. At higher pressures the direct Tb3+ → Eu3+ energy transfer is strongly enhanced, resulting in an initial non-exponential decay. Consistent with a dominant energy diffusion process, the decay time of the following exponential part decreases with increasing pressure due to decreasing average distances to the Eu3+ ions. In summary, the work of Blanzat et al. (1984) supports the conclusions of Merkle et al. (1981) who identiﬁed the energy migration mechanism as the dominant energy transfer mechanism in NdP5 O14 . In the beginning of sect. 5.3 it was mentioned that besides depletion processes due to enhanced non-radiative decay, ﬁlling processes due to some long-living reservoir may also occur. La2 O2 S doped with Eu3+ represents such a case. Two types of traps are responsible there for the slow energy release, one type forming a shallow and the other a deep storage. The phosphorescence of this material was studied by Webster and Drickamer (1980b) under pressures up to 6 GPa. They approximated the decay curves of the Eu3+ luminescence as the sum of two exponential terms, belonging to the shallow and deep traps, respectively. Under pressure they observed an increase of both lifetimes of the detrapping processes. These lifetimes depend on the activation energy necessary for detrapping and thus can be used to determine the activation energy as a function of pressure. In their study, Webster and Drickamer (1980b) found that both activation energies increased under pressure. It was argued that the formation of the charge transfer state represents the detrapping process. This assumption is supported by the high pressure studies where energy could be stored in the traps at high pressure for an apparently indeﬁnite length of time and appeared as emission from the Eu3+ ion on the sudden release of pressure, a phenomenon similar to thermoluminescence. A technological interesting possibility is the energy transfer from transition-metal ions to f elements. Transition-metal ions offer broad absorption bands which can be easily excited by ﬂashlamps. A subsequent energy transfer to an f element can then result in a sharp emission

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Fig. 18. Schematic energy level diagrams of Cr3+ and Tm3+ in YAG showing the energy transfer from Cr3+ to Tm3+ . The absorption and luminescence spectra of YAG:Cr3+ (0.5 at.%) are shown at ambient pressure and room temperature (from Shen et al. (2000)).

in the near infrared. Such a process may be used to develop efﬁcient laser materials. A typical system of this type is Cr3+ :Tm3+ :Y3 Al5 O12 (YAG). This material has been studied under high pressure by Wamsley and Bray (1994a, 1995) and Shen et al. (2000). A schematic energy-level diagram of Cr3+ and Tm3+ in YAG together with the luminescence and absorption spectra of Cr3+ are shown in ﬁg. 18. Three primary Cr3+ → Tm3+ energy transfer pathways can be identiﬁed: thermally activated energy transfer from the 4 T2 state (4 T2 ET), thermally activated energy transfer from the 2 E anti-Stokes phonon sidebands (2 E anti-Stokes ET), and temperature-independent energy transfer from the zero phonon and Stokes phonon sidebands of the 2 E state (2 E Stokes ET). In a ﬁrst step Shen et al. (2000) studied the temperature dependence of the Cr3+ luminescence. Setting up the dynamic rate equations for the Cr3+ –Tm3+ system, the number ND of Cr3+ donor ions in the thermally coupled 4 T2 –2 E excited states can be calculated according to ND (t) = ND (0)e−WD t e−PDA (t )

with PDA (t) = Ns ln 1 − CA + CA e−WDA (Rs )t .

(23)

s

Here ND (0) is the number of donors excited at t = 0, WD is the intracenter decay rate of the coupled 4 T2 –2 E states of Cr3+ , CA is equivalent to the acceptor doping concentration, Ns is

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the number of equivalent acceptor sites in the coordination shell s at a distance Rs from the donor, and WDA (Rs ) is the donor–acceptor transfer rate which is assumed to be the same for all acceptor ions in the same shell s. In their analysis, Shen et al. (2000) took into account the ﬁrst eight acceptor coordination shells of the Cr3+ ion and a dipole–dipole energy transfer mechanism. For an accurate description of the decay curves of the Cr3+ luminescence, it was shown that all three transfer pathways described above had to be taken into account. In particular, three temperature regions could be distinguished by the relative weight of the pathways: at temperatures below ∼ 75 K neither the 4 T2 state nor the 2 E anti-Stokes phonon sidebands contributed signiﬁcantly to the decay, resulting in a constant WDA transfer rate due to 2 E Stokes ET. With increasing temperature the increasing 2 E anti-Stokes phonon sidebands lead to an enhanced transfer rate. With further increasing temperature above ∼ 175 K the thermal population of the 4 T2 state becomes appreciable, resulting in a even stronger increase of the energy transfer rate. The temperature dependence of the energy transfer rate WDA is related to a changing occupation of the 2 E anti-Stokes phonon sidebands and the 4 T2 state. On the contrary, pressure signiﬁcantly increases the energy separation between the 4 T2 and 2 E states, whereas the energy of the zero phonon and the vibronic 2 E → 4 A2 transitions of Cr3+ change only weakly with pressure. Thus, pressure almost solely inﬂuences the occupation of the 4 T2 state and with it its contribution to the energy transfer rate, but does not affect the other contributions connected with the 2 E state. According to these considerations, Shen et al. (2000) took advantage of this situation by artiﬁcially eliminating the energy transfer due to the 4 T2 state by the application of high pressure. They ﬁrst studied the decay curves of the Cr3+ luminescence under pressure at room-temperature and analyzed them with eq. (23). Assuming again a dipole–dipole transfer mechanism and taking into account the ﬁrst eight acceptor coordination shells, they obtained the Cr3+ → Tm3+ transfer rate WDA as a function of pressure, as shown in ﬁg. 19.

Fig. 19. Room temperature Cr3+ → Tm3+ transfer rate WDA in Cr3+ (0.7 at.%):Tm3+ (2 at.%):YAG as a function of pressure (from Shen et al. (2000)). WDA was obtained from ﬁts to the experimental decay curves at different pressures assuming dipole–dipole energy transfer. The solid line has been calculated as described in the text. (10 kbar = 1 GPa).

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The pressure dependence of WDA can be divided into different regions. From ambient pressure to around 4 GPa a very fast decrease of the transfer rate can be noted. This range corresponds to the decreasing occupation of the 4 T2 state with increasing energy separation under pressure. Above approximately 6 GPa a leveling off can be observed, indicating that now only the temperature and pressure independent part of the 2 E Stokes ET contribute to the transfer rate. The solid curve in ﬁg. 19 represents a calculation of the transfer rate taking into account the three pathways for energy transfer and the pressure-induced increase of the energy separation (Wamsley and Bray, 1994b). Obviously a very good agreement with the data was obtained. The importance of the three different pathways for energy transfer can now be isolated by considering three cases: (1) The limiting transfer rate at ambient pressure and low temperatures WDA ∼ 10 ms−1 can be regarded as a measure for 2 E Stokes ET. (2) The limiting high-pressure transfer rate at room temperature WDA ∼ 95 ms−1 contains 2 E Stokes ET as well as 2 E anti-Stokes ET. Because both contributions do not change with pressure, they can be directly related to ambient pressure room temperature conditions. (3) The ambient pressure, room temperature rate of WDA ∼ 400 ms−1 represents a sum of all three contributions. Subtracting the value obtained in case two directly indicates the importance of the 4 T2 ET part. Finally, in a last step Shen et al. (2000) also analyzed the spectra and decay curves of the Tm3+ ions. On the basis of the luminescence spectra they noted that Tm3+ ions located in the ﬁrst coordination shell of the Cr3+ ions (C-type) showed a distinctly different spectral pattern compared to the almost similar patterns of more distant Tm3+ ions (N’-type). Studying the decay curves of both types of Tm3+ ions at different temperatures, they could show that the energy transfer from the Cr3+ ions to the C-type ions is much faster than to the N’-type ions. However, at room temperature the energy transfer to the N’-type ions dominate, which is due to an overall strongly increased energy transfer (participation of the 4 T2 state) and a saturation of the transfer to C-type ions. This case is described by the Inokuti–Hirayama model for energy transfer, where a random distribution of acceptor sites is assumed (Inokuti and Hirayama, 1965). At higher pressures, where the energy transfer due to the 4 T2 state is eliminated again, the overall transfer rate decreases and thus the energy transfer to the C-type ions gains importance. Similar to the low-temperature case, the Inokuti–Hirayama model then starts to breakdown because the inherent assumptions of the model are no longer fulﬁlled. 5.3.4. Energy transfer processes in semiconductors In the case of semiconductors doped with f elements a different kind of an energy transfer process can be observed, namely from extended band states or excitonic states to the highly localized f-element states. Such a process is different from the cases discussed in the preceding sections, where the energy transfer from point defects (or at the most molecular states) was considered. The interest in semiconductors doped with f elements is obvious, because of their potential to combine sharp f-element luminescence with the possibility of simple electrical excitation via the semiconductor host. However, a quenching of the luminescence with

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Fig. 20. Energy back-transfer model describing the energy transfer between the semiconductor host and the lanthanide ion R 3+ (Culp et al., 1997; Takarabe et al., 1995).

increasing temperature and the very low efﬁciencies found for f elements in semiconductors already at room temperature, prevented them from the use as opto-electronic devices. To address the problem of low efﬁciencies, one needs a better understanding of the nature of f-element centers in the semiconductor lattice, their energy level structure in relationship to the host band structure and the relevant excitation mechanisms. In this respect, high pressure offers the unique possibility to study energy transfer processes while continuously shifting the host band edges with respect to the f-element energy levels. Despite this advantage, only few systems have been studied under pressure so far. These include some systems doped with the Er3+ ion, where the technological interest is due to the emission in the infrared region at 1.54 μm, a wavelength which matches the minimum loss of silica ﬁbers. Another system is InP:Yb3+ which has the advantage that the Yb3+ ions form only one kind of luminescence centers in the InP host and in addition, with only one f-electron missing in the 4f shell, Yb3+ possesses the simplest electronic structure of all f elements. The excitation mechanism of the f elements in semiconductors can be illustrated by ﬁg. 20. Through carrier injection or a host photoexcitation process electrons and holes are created. The f element, acting as an electron or hole trap catches a carrier and becomes negatively or positively charged. The Coulombic potential of the charged center subsequently attracts a further carrier of opposite charge, leading to an exciton bound at the f-element center. Finally, the exciton transfers its energy to the 4f-shell by a nonradiative recombination. Taking into account an energy back-transfer mechanism as indicated in ﬁg. 20 it was also possible to explain the observed temperature quenching of the f-f luminescence in InP:Yb3+ as well as in GaAs:Er3+ . During the energy back-transfer process at higher temperatures, the energy of the excited rare-earth ion is used to once again create an e-h pair by phonon-assisted nonradiative recombination (a variety of the Auger effect) at the rare-earth ion (Taguchi et al., 1994). This e-h pair can then recombine or completely dissociate and thus quench the f-f luminescence. A ﬁrst test of this model was performed with pressure experiments on InP:Yb3+ . Here the Yb3+ ion introduces an electron trap to the semiconductor host. The pressure-induced shift of the 2 F5/2 → 2 F7/2 intra 4f shell transitions amounts to 0.96 meV/GPa up to 4 GPa (Stapor et al., 1991), while the bandgap energy of InP increases by 85 meV/GPa (Trommer et al., 1980).

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Fig. 21. Change of the Yb3+ trap level under pressure. The Yb3+ ground state is arbitrarily aligned with the valence band (Culp et al., 1997; Takarabe et al., 1995).

This behavior is schematically shown in ﬁg. 21, where the change in the 2 F5/2 –2 F7/2 splitting, being about two orders of magnitude smaller than the bandgap rise, has been neglected. Two energies in ﬁg. 21 are important quantities for the luminescence behavior. First, the energy ET represents the binding energy of the rare earth bound exciton with respect to the conduction band and second, EBT , the necessary energy for back-transfer, corresponds to the difference between the bound exciton recombination energy and the 2 F5/2 → 2 F7/2 transition energy of the Er3+ ion. Assuming a thermal equilibrium between the bound e-h pairs and the excited Yb3+ ions, the intensity ratio of the band-edge related emission IInP due to the bound e-h pairs and the Yb3+ luminescence IYb depends on the energy EBT (Takarabe, 1996). Measuring the variations of the intensity ratio IInP /IYb under pressure, Takarabe (1996) was able to determine the energy difference EBT and found a pressure-induced shift of 70 meV/GPa which is close to the shift of the band-edge related luminescence due to the bound e-h pairs. Furthermore, under pressure it was possible to completely recover the thermally quenched luminescence of the Yb3+ ion at temperatures of 220 K and 260 K (Takarabe et al., 1994) as well as at room temperature (Takarabe, 1996). The minimum pressure at which the luminescence could be observed again was shown to increase with increasing temperature. All these facts ﬁtted well to the proposed back-transfer model, which was thus strongly supported by the pressure experiments. The same model has been applied also to GaAs:Er3+ (Takarabe et al., 1995, 1997; Hogg et al., 1997b; Culp et al., 1997) under pressure. In addition to the intensity measurements, Culp et al. (1997) also studied the lifetime of the 4 I13/2 → 4 I15/2 transition of Er3+ in GaAs. At ambient pressure, a temperature study revealed that the lifetime at ﬁrst did slightly increase with increasing temperature, although the intensity was already decreasing. Only above 150 K did the lifetime start to decrease. This result is still consistent with the back-transfer model if additionally the dissociation of the bound exciton is taken into account. This process requires a second different activation energy which is needed to remove the Coulombic bound hole from the negatively charged trap. The dissociation can occur already at lower temperatures, preventing the energy transfer from the exciton to the f element. Accordingly, only the intensity, but not the lifetime changes. At higher temperatures the back-transfer process is added to the dissociation which then decreases both intensity and lifetime. To account for both processes under pressure, Culp et al. (1997) considered a two-process quenching model

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of the form: X=

X0

E1

E2 , + A2 exp − kT 1 + A1 exp − kT

(24)

where E1 and E2 denote the activation energies and X is either the intensity or the lifetime of the Er3+ luminescence. As the result they obtained E1 = 13.4 ± 0.3 meV, which was assigned to the exciton dissociation process and E2 = 115.8 ± 3.4 meV, which was assigned to the back-transfer process. Under a pressure of 4.2 GPa, the quenching of the luminescence was reduced by nearly an order of magnitude at room temperature, an observation which is identical to the case of InP:Yb3+ (Takarabe, 1996). A further ﬁt of the activation energies at 4.2 GPa gave an almost constant value for E1 = 10.4 ± 3.0 meV, a result which ﬁts to the assumption of this activation energy being due to the Coulombic electron-hole binding energy. The change of the second activation energy was estimated to lie between +6 and +50 meV/GPa. This value is very uncertain due to the already weak effects of the backtransfer process. However, it is comparable to the experimental shift found for the Er3+ related trap in GaAs:Er,O of 36 meV/GPa (Takarabe et al., 1995) and to theoretical calculations, giving values of 24 meV/GPa (Chadi and Chang, 1988) and 10–40 meV/GPa (Ren et al., 1982). The luminescence intensity of the Er3+ ion under pressure has also been studied in Si. This semiconductor possesses an indirect bandgap, contrary to the cases discussed above. At ambient pressure, the 4f-4f luminescence of the Er3+ ion in Si is quenched at temperatures exceeding 100 K, but contrary to the case of direct bandgaps, indirect bandgaps decrease with increasing pressure. Therefore, provided the energy back-transfer model can be applied here, the observed quenching temperature for the Er3+ ion should decrease under pressure. In highpressure experiments, Przybylinska et al. (1996) and Jantsch et al. (1996) observed exactly the opposite, namely an increase of the quenching temperature with pressure. However, this behavior was not attributed to a breakdown of the back-transfer model but to the existence of deep oxygen related levels which mediated the energy transfer process. As in the case of Si, GaP is also a semiconductor with an indirect bandgap. Culp et al. (1996) have studied the Er3+ ion doped into GaP under pressures up to 5 GPa. Contrary to the cases discussed above, the Er3+ luminescence does not show a pronounced quenching with increasing temperature. In addition, the Er3+ emission intensity is considerably stronger when exciting with below-bandgap energies, which promotes carriers directly to the Er3+ related trap, than with above-bandgap energies, where the free carriers which are created subsequently have to be captured by the Er3+ trap. Under pressure, the above-bandgap excitation became as effective as the below-bandgap excitation. This behavior was explained by the fact that competitive capture of free carriers by deep levels, responsible for the lower efﬁciency for above-bandgap excitation at ambient pressure, is signiﬁcantly reduced with increasing pressure. 6. Electron–phonon interaction In general, due to the localized and screened nature of the 4f-electrons, their interaction with phonons is weak. However, this interaction affects the 4f states in many different ways and

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can give important contributions in speciﬁc cases. In principle, the interaction inﬂuences the energy levels as well as the transition probabilities between different states. A quite common feature is the thermal line broadening, however, the energy levels can also be shifted or split by the electron–phonon interaction. Furthermore, transitions between 4f states involving the creation or annihilation of phonons (phonon sidebands) can be observed. A pronounced effect on the intensities can be noted also for speciﬁc transitions where the luminescence can be quenched completely via nonradiative transitions through multiphonon relaxation or a quenching process involving charge transfer states or 4fN−1 5d1 conﬁgurations (see sects. 5.3.1 and 5.3.2). On the other hand, phonons in crystals with a rare-earth site symmetry including an inversion center, can be the only source to mix conﬁgurations with an odd parity to the 4f-states and thus allow for the zero-phonon transitions. In sects. 5.3.1 and 5.3.2 the electron–phonon coupling was necessary to mediate an energy transfer process but no attempt was made to discuss the coupling strength between an electronic level and a lattice vibration itself. In fact, this coupling strength has been the subject of very few high pressure studies and thus will be considered only brieﬂy in this section. One of the ﬁrst studies was performed by Voloshin (1986), who reported on the intensity changes of vibronic lines for Pr3+ in lanthanum ethylsulfate under pressures up to 2.5 GPa. Furthermore, a qualitative experiment has been presented by Shen and Holzapfel (1993), who studied the phonon sidebands of the transitions 5 D0 → 7 F1,2 and 5 D1 → 7 F1 of the Sm2+ ion in BaFCl under pressures up to 8 GPa at 20 K. The bandshape of the sidebands was similar for all transitions, however, they noted a strong enhancement of the phonon sidebands under pressure solely for the 5 D1 → 7 F1 transition. This enhancement reﬂected an increasing electron–phonon coupling under pressure. Changing electron–phonon couplings have been observed also for Cs2 NaTmCl6 . In this case the relative intensities of different Raman lines showed an anomalous behavior under pressure, which has been qualitatively interpreted as due to an electron–phonon coupling of the aΓ5 electronic state with the Γ1 + ν5 (t2g ) vibronic state (Mak et al., 2002). Likewise qualitative studies have been performed for two different glasses. Lochhead and Bray (1995) used high pressure to characterize the local structure of Eu3+ ions in sodium disilicate glass. Their luminescence and lifetime studies revealed two different pressure regimes with different behavior of intensities and lifetimes. In the high-pressure regime from 4 GPa to the maximum pressure of 21 GPa achieved in their experiment, a decrease of the 5 D0 → 7 F0 lifetime from approximately 2.5 ms down to 1.4 ms is accompanied by a decrease in the luminescence signal and an increase in the linewidth. These observations could be explained by an enhanced nonradiative decay under pressure, which in turn was related to an increased coupling to local vibrations because of shorter Eu–O bonds. Similar results were reported by Jayasankar et al. (2000) in a high pressure study on Sm3+ in lithium ﬂuoroborate glass. They also attributed a decrease in the decay time of the 4 G(4)5/2 → 6 HJ transition from 1.3 ms at ambient pressure to 0.6 ms at 21 GPa to an increased coupling to local vibrations. The electron–phonon interaction has been studied also in a LiTmF4 crystal by Kupchikov et al. (1982). They have measured Raman and infrared reﬂection spectra under pressures up to 1.2 GPa and at temperatures ranging from 4.2 K to 300 K. The interaction of optical phonons with electronic excitations in this system of rare-earth ions was detected by anomalous tem-

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Table 11 Bare crystal-ﬁeld (CF) and phonon (ph) energies and the CF–phonon coupling constant V at ambient pressure and the corresponding pressure coefﬁcients for the compounds NdBa2 Cu3 O7 and Pb2 Sr2 NdCu3 O8 (Goncharov et al., 1994). CE and SC refer to ceramic and single-crystal samples, respectively Substance Pb2 Sr2 NdCu3 O8 SC NdBa2 Cu18 3 O7 CE NdBa2 Cu16 3 O7 CE NdBa2 Cu3 O7 SC

νCF (cm−1 ) 319 295 300 297

dνCF /dP (cm−1 /GPa) 3.47 3.0 2.68 2.46

νph (cm−1 ) 293 293 308 307

dνph /dP (cm−1 /GPa) 2.67 3.0 2.37 2.80

V (cm−1 ) 25.5(4) 25 26.7(3) 28.1(3)

dV /dP (cm−1 /GPa) 0.29(7) – 0.16(3) 0.26(4)

perature and pressure dependences of some lines in the lattice vibration spectra. Using a microscopic theory, Kupchikov et al. (1982) could determine binding parameters between rareearth ions and optical phonons and use these parameters to estimate shifts in lattice vibrational lines as a function of temperature and pressure. A quantitative analysis of the electron–phonon coupling was performed by Goncharov et al. (1994) on the Nd-containing cuprates NdBa2 Cu3 O7 and Pb2 Sr2 NdCu3 O8 . Here the effect of pressure on the coupling between a Nd3+ crystal-ﬁeld excitation and a CuO2 -plane oxygen phonon (B1g ) near 300 cm−1 was investigated up to 14 GPa. In both samples the interaction between an excited level of the 4 I9/2 ground multiplet and the out-of-plane oxygen vibration leads to a doublet structure in the Raman spectra. While in the case of NdBa2 Cu3 O7 the bare crystal-ﬁeld excitation is lower in energy than the phonon frequency, the opposite is found for Pb2 Sr2 NdCu3 O8 . The motivation of the high-pressure experiments arose from the fact that the application of pressure results in simultaneous changes of the crystal-ﬁeld and phonon energies and their energy differences. From the frequencies and intensities of the coupled excitations under pressure, it is possible to derive the pressure dependence of the bare crystal-ﬁeld energy level and the coupling constant using a two-level coupling model (Thalmeier and Fulde, 1982). The change of the coupling constant can subsequently be related to the corresponding changes of the interatomic distances. According to the two-level coupling model, the bare crystal-ﬁeld excitation ωCF and phonon ωph frequencies and the coupling constant V can be expressed as 1 ν1 k + ν2 ν1 + ν2 k , ωph = and V = · (ν1 − ν2 )2 − (ωph − ωCF )2 , (25) ωCF = 1+k 1+k 2 where ν1 and ν2 denote the line positions and k is their oscillator strength ratio. The results for the pressure-induced changes of the bare energies and the coupling constant are summarized in table 11. It is obvious that the crystal-ﬁeld splittings as well as the electron–phonon coupling increase with increasing pressure for both samples, regardless of the relative ordering of the bare crystal-ﬁeld level and the phonon energy. 7. Conclusions The development of the diamond anvil cell opened an easy, fast, and reliable possibility to study optical spectra as a function of applied pressure. With this elegant method, the energy

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level scheme, transition probabilities and intensities, energy transfer processes and many other properties of ions in crystals can be related to the structural parameters of the host lattice. Besides the structural relationship, an important feature concerns the ability of pressure to “tune” energies of various electronic states in a different manner. This allows to alter energy differences and to explicitly study their respective inﬂuence on the state under investigation. While ambient pressure studies must rely on discrete changes of crucial parameters, the high pressure method is capable of generating continuous changes of interatomic distances or relative energies of different electronic states. Moreover, at the same time the chemical composition of the rare-earth compound is conserved under pressure, while ambient pressure studies usually have to consider different compounds. In this sense, the application of high pressure can solve physical problems which can not be accessed by any other method. The main emphasis in this chapter was put on the optical investigations under high pressure. These studies reveal a considerable part of the energy level scheme and can be used also to study lifetimes and intensities. All these quantities are related to and inﬂuenced by the electronic states of the other constituents in the crystal. However, it should be noted that many other physical methods have been employed in connection with high-pressure devices. Although the high-pressure method itself is rather simple to use, high-pressure physics is still a somewhat “exotic” tool for investigating rare-earth compounds. This seems rather surprising if the unique possibilities for example for the determination of intrinsic crystalﬁeld parameters are considered. In many cases, theories explicitly predict certain distance dependences, which can be veriﬁed straightforward by the application of pressure, which continuously alters the interatomic distances. The knowledge of fundamental relations between the properties of rare earths and the electronic and physical structure of the host compound is essential for the development of improved or new materials. However, up to now only a rather small amount of high-pressure studies compared to ambient pressure studies has been performed. It is hoped that this chapter has demonstrated the ability of high-pressure physics in exploring fundamental relationships especially for rare-earth ions and will stimulate further experimental and theoretical work in this area. Acknowledgement Financial support under grants from the Deutsche Forschungsgemeinschaft (DFG) is gratefully acknowledged. The author wishes to thank W.B. Holzapfel (Universität Paderborn, Germany) for his continuous support during the past years and W. Sievers (Universität Paderborn, Germany) for editorial help. References Arashi, H., Ishigame, M., 1982. Jpn. J. Appl. Phys. 21, 1647. Asaumi, K., Ruoff, A.L., 1986. Phys. Rev. B 33, 5633. Auzel, F., 1976. IEEE J. Quantum Electron. QE-12, 258.

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AUTHOR INDEX Aarts, J., see Fäth, M. 298 Aas, W. 500 Abbasov, A.S., see Geydarova, E.N. 85 Abd-Elmeguid, M.M., see Bauer, E. 24 Abdusalamova, M.N. 36, 37, 135 Abdusalamova, M.N., see Abulkhaev, V.D. 37, 94 Abe, H., see Katsumura, Y. 489, 496, 497, 508 Abe, K., see Aoki, Y. 17–19 Abe, K., see Keller, L. 17, 23 Abe, K., see Sugawara, H. 18 Abe, R., see Park, Y.Y. 489, 491, 492, 498 Abe, Y., see Sato, H. 6, 8, 12, 17, 18, 22, 23 Abe, Y., see Sugawara, H. 8, 9, 23 Abraham, M.M., see Chen, G. 523, 524 Abrikosov, N.Kh., see Dudkin, L.D. 29 Abulkhaev, V.D. 37, 94 Achard, J.C., see Ravot, D. 57 Adachi, G., see Jiang, J. 479, 483, 494 Adachi, T., see Shirotani, I. 7–9, 12 Adamo, C. 183, 186–189 Adams, C.P. 298 Adams, H., see Platas, C. 358, 359, 377, 378, 400–404 Adams, M.J. 470 Addleman, R.S. 489, 509 Adler, P., see Loa, I. 268 Adroja, D.T. 60, 61, 118 Adroja, D.T., see Malik, S.K. 48, 56, 60, 69, 77, 81, 85, 89, 108, 118 Adroja, D.T., see Thornton, M.J. 124 Afanas’ev, Y.A., see Khanaev, E.I. 209, 213 Afanas’ev, Y.A., see Storozhenko, T.P. 215–217 Agmon, N. 489 Ahn, K.H. 267, 268 Ahn, K.H., see Quijada, M.A. 296 Ahnen, T., see Petzel, T. 234, 235 Aime, S. 357, 360–363, 420–422, 426, 429, 433, 439, 440 Aime, S., see Benetollo, F. 420 Aime, S., see Bruce, J.I. 355 Aime, S., see Marques, M.P.M. 421, 423 Aime, S., see Zhang, S. 355 Ajtony, Z., see Kaposi, O. 196, 240

Akishin, P.A. 224 Akita, K., see Sekine, C. 13 Al-Souﬁ, W. 471, 498 Alascio, B., see Causa, M.T. 326 Albering, J.H. 76, 90 Albin, M. 478, 499, 505 Albin, M., see Horrocks Jr., W.deW. 507 Albrecht-Gary, A.M., see Nehlig, A. 473, 474, 482, 485 Aldred, A.T., see Shaked, H. 84, 87, 89, 90, 127, 129 Aléonard, S., see Labeau, M. 203 Alexandrov, A.S. 308 Algarabel, P.A., see De Teresa, J.M. 298–300 Aliev, F.G. 118 Aliev, I.I., see Sadygov, F.M. 75 Aliev, O.M. 55, 77, 78, 80, 91, 92 Aliev, O.M., see Rustamov, P.G. 74, 77, 92 Aliyev, I.Ya., see Geydarova, E.N. 85 Aliyev, O.M., see Sadygov, F.M. 36 Allegrozzi, M. 363 Allen, P. 474 Allen, P.B. 268, 269 Allen, P.B., see Chen, Y.-R. 285 Allen, P.B., see Perebeinos, V. 268 Allendoerfer, R.D., see Reilley, C.N. 357, 406 Allenspach, P., see Mesot, J. 524, 535 Allodi, G. 288, 325, 328, 337 Allodi, G., see Cestelli Guidi, M. 264 Allsopp, S.R. 473, 474 Almai, M., see De Kozak, A. 202 Alonso, J. 324 Alonso, J.A., see Frontera, C. 336 Alonso, J.M., see Fernández-Díaz, M.T. 329 Alpoim, M.C., see Geraldes, C.F.G.C. 410 Alsaadi, B.M. 361, 405–407 Altmeyer, R.O. 37 Amato, A., see Cestelli Guidi, M. 264 Amayri, S., see Bernhard, G. 495 Amelichev, V., see Shames, A.I. 338 Ameloot, M., see Beechem, J.M. 498 Ameloot, M., see Janssens, L.D. 471 591

592

AUTHOR INDEX

Ameloot, M., see Molski, A. 489, 502 Amin, S. 426 Amin, S., see Morrow, J.R. 426 Amis, E.S., see Hinton, J.F. 493 Amitsuka, H., see Sekine, C. 20 Ammon, W.v., see Yersin, H. 523, 569 An, Y. 405, 481, 483, 494 Anane, A. 291 Anane, A., see Raquet, B. 326 Anderson, P.W. 31, 256, 258 André, G. 123 André, G., see Autret, C. 338 André, G., see Damay, F. 330, 336 André, N., see Platas-Iglesias, C. 406, 407 Andreev, A.V., see Matsuda, T.D. 17 Andres, K., see Neumeier, J.J. 278 Anelli, P.L., see Aime, S. 433 Ansoborlo, E., see Billard, I. 470, 495, 501–503, 506 Ansoborlo, E., see Scapolan, S. 508 Antonio, M.A., see Xue, J.S. 12 Aoki, K., see Sugawara, H. 18 Aoki, Y. 17–19 Aoki, Y., see Keller, L. 17, 23 Aoki, Y., see Matsuda, T.D. 17 Aoki, Y., see Sato, H. 6, 8, 12, 17, 18, 22, 23 Aoki, Y., see Sugawara, H. 8, 9, 23 Aoyagi, H., see Nagaishi, R. 497 Apperson, K., see Billard, I. 470, 495, 501–503, 506 Arai, F., see Kimura, S. 130 Arashi, H. 524, 529, 553, 554 Arashi, H., see Yusa, H. 523, 553 Archibald, W. 294, 295, 300 Archibald, W., see Zhou, J.-S. 300–302 Argyriou, D.N., see Radaelli, P.G. 299, 323 Arima, T. 279 Arima, T., see Asamitsu, A. 319 Arima, T., see Murakami, Y. 263 Arima, T., see Urushibara, A. 311 Arima, T., see Zimmermann, M.V. 264 Arisaka, M. 473, 474, 481 Arispe, J., see Mayr, M. 326 Arkle, V.K., see Horrocks Jr., W.deW. 499, 501 Armitage, J.G.M., see Thornton, M.J. 124 Arnold, Z., see De Teresa, J.M. 298, 300 Arnott, R.J., see Goodenough, J.B. 265, 267, 269, 270 Arnott, R.J., see Wold, A. 289 Arpigny, S., see Billard, I. 470, 495, 501–503, 506 Arroyo, A., see Alonso, J. 324

Arsenov, A.A., see Adams, C.P. 298 Arsenov, A.A., see Senis, R. 317 Arsenov, A.A., see Vasiliu-Doloc, L. 321 Artem’eva, M.V., see Yudin, V.M. 276 Arulraj, A., see Rao, C.N.R. 330 Arvis, M. 497 Asamitsu, A. 291, 319 Asamitsu, A., see Kuwahara, H. 333, 337 Asamitsu, A., see Moritomo, Y. 311 Asamitsu, A., see Okuda, T. 325 Asamitsu, A., see Saitoh, E. 321 Asamitsu, A., see Tokura, Y. 330, 341 Asamitsu, A., see Tomioka, Y. 291, 294, 297 Asamitsu, A., see Urushibara, A. 311 Asamitsu, A., see Zhou, J.-S. 311 Asaumi, K. 519 Ashworth, H., see Sharman, K.S. 470 Assefa, Z., see Morrison, H.G. 151, 205 Assefa, Z., see Yersin, H. 523, 569, 570 Atabekyan, L.S., see Billing, R. 489, 491 Atwood, J.L., see Steed, J.W. 355 Aune, R.E., see Stolyarova, V.L. 235 Aupiais, J. 508 Aury, S., see Giroux, S. 494, 505 Austin, A.E., see Wood, V.E. 275 Autret, C. 338 Auzel, F. 573 Avecilla, F., see Platas, C. 358, 359, 377, 378, 400–404 Averitt, R.D., see Lobad, A.I. 326 Ayala, J.D., see Aime, S. 420 Azehna, A.E., see Billard, I. 470, 495, 501–503, 506 Azenha, M.E. 498 Azuma, N., see Matsumoto, A. 506 Babailov, S.P. 357 Babu, P., see Jayasankar, C.K. 522, 581 Babushkina, N., see Yakubovskii, A. 309 Babushkina, N.A. 308, 309, 327 Bäckström, J., see Björnsson, P. 268 Baetslé, L.H. 149 Baev, A.G., see Novikov, G.I. 236 Baginskii, A.V., see Lyapunov, K.M. 164, 165, 176 Bagirova, S.D., see Geydarova, E.N. 85 Baglio, J.A., see Struck, C.W. 196 Baird, C.P. 497, 498 Baker, F.B. 214 Baker, M.V. 356 Balakrishnan, G., see Allodi, G. 328, 337 Balakrishnan, G., see Campbell, A.J. 319

AUTHOR INDEX Balakrishnan, G., see Heffner, R.H. 325 Balakrishnan, G., see Lees, M.R. 291 Balakrishnan, G., see Zvyagin, S. 338 Balbashov, A.M., see Mayr, F. 315 Balbashov, A.M., see Smolyaninova, V.N. 321 Balcells, Ll., see Martínez, B. 317 Balthazar, K., see Kaposi, O. 196, 240 Balu, N., see Monteil, A. 524, 556 Balzani, V. 355, 471 Balzani, V., see Sabbatini, N. 494 Bandyopadhyay, B., see Mandal, P. 312 Banerjee, A.K., see Fronczek, F. 381 Bao, W., see Schiffer, P. 328 Barbero, L., see Aime, S. 357, 361, 363, 421, 422 Bare, W.D. 470, 509 Barge, A., see Aime, S. 420, 422, 426, 429 Barnett, J.D. 522, 552, 554 Barnett, J.D., see Piermarini, G.J. 518, 519 Barone, V., see Adamo, C. 186, 189 Barratt, J., see Lees, M.R. 291 Barry, C.D. 363 Barthelemy, P.P. 478, 479 Bartholin, H., see Burlet, P. 55 Bartholin, H., see Rossat-Mignod, J. 55, 57 Barthou, C., see Blanzat, B. 523, 524, 574 Basch, H., see Stevens, W.J. 148 Baskaran, G., see Zhao, Y.G. 296 Basov, D.N., see Dilley, N.R. 26 Basov, D.N., see Dordevic, S.V. 8, 12, 17, 26, 27 Batlogg, B., see Hwang, H.Y. 290, 291 Batlogg, B., see Radaelli, P.G. 323, 325 Batsanov, A., see Parker, D. 420 Baudelet, F., see Tolentino, H. 518 Bauer, E. 24 Bauer, E.D. 8, 12, 13, 15–17, 21, 22, 24 Bauer, E.D., see Dilley, N.R. 15, 26 Bauer, E.D., see Dordevic, S.V. 8, 12, 17, 26, 27 Bauer, E.D., see Gajewski, D.A. 13 Bauer, E.D., see Maple, M.B. 22 Baumann, M. 524 Bazin, H. 509 Bazzicalupi, C. 492, 509 Beale Jr., A.F., see Westrum Jr., E.F. 154, 157 Beaucaire, C., see Moulin, C. 508 Beaudry, B.J., see Spedding, F.H. 164, 165, 176, 178 Beck, H.P. 558, 559 Beck, H.P., see Bolduan, F. 522, 550, 566 Beck, H.P., see Shen, Y.R. 564 Becke, A.D. 148 Beeby, A. 481–484

593

Beeby, A., see Clarkson, I.M. 484, 505 Beechem, J.M. 498 Begun, G.M., see Daniel, J.F. 151, 205 Begun, G.M., see Del Cul, G.D. 523 Begun, G.M., see Haire, R.G. 558 Begun, G.M., see Peterson, J.R. 558 Begun, G.M., see Wilmarth, W.R. 521, 522, 558 Begun, G.M., see Young, J.P. 558 Beitz, J.V. 473, 478, 495, 497, 501 Belesi, M., see Papavassiliou, G. 325, 326 Bell, J. 497 Bell, P.M. 519 Bell, P.M., see Mao, H.K. 518 Belova, L.M., see Babushkina, N.A. 308, 309, 327 Bencini, A., see Bazzicalupi, C. 492, 509 Bencze, L. 186, 226, 235 Benedict, U., see Haire, R.G. 558 Benedict, U., see Peterson, J.R. 522, 558 Benedict, U., see Syassen, K. 550 Benetollo, F. 420 Benetollo, F., see Aime, S. 420, 422 Bennington, S., see Keppens, V. 11 Bensaid, A., see Reutler, P. 326 Berezhkovskii, A.M. 489 Berger, S., see Bauer, E. 24 Bernard, C., see Monteil, A. 524, 556 Bernard, O., see Simonin, J.P. 491 Bernardinelli, G., see Bocquet, B. 453, 455, 456 Bernardinelli, G., see Floquet, S. 453, 455–459 Bernardinelli, G., see Piguet, C. 355, 384, 385, 393–395 Bernardinelli, G., see Renaud, F. 387–393, 408 Bernardinelli, G., see Rigault, S. 358, 361, 363, 366, 378, 396–400 Bernhard, G. 495 Bernhard, G., see Brendler, V. 499 Bernhard, G., see Geipel, G. 495, 499, 500, 505 Bernhard, G., see Rutsch, M. 501 Berni, E., see Bazzicalupi, C. 492, 509 Berny, F. 358 Berregi, I. 507 Berry, M.T., see An, Y. 405, 481, 483, 494 Bertaut, E.F. 258 Bertaut, E.F., see Quezel, S. 275 Berthoud, T. 507, 508 Bertini, I. 356, 357, 359, 361–364, 366–368, 374 Bertini, I., see Allegrozzi, M. 363 Bertram, S., see Hu, Z. 521 Besenbruch, G., see Kent, R.A. 234 Besenbuch, G. 235 Besson, J.M., see Gonzalez, J. 518

594

AUTHOR INDEX

Bethe, H.A. 526 Bettonville, S. 217, 219, 221 Bhat, S.V., see Joshi, J.P. 336 Bi, Q. 523, 529, 553 Bianchi, A. 426 Bianchi, A., see Bazzicalupi, C. 492, 509 Bianconi, A., see Lanzara, A. 295, 325 Bidoglio, G., see Eliet, V. 474, 498, 501 Biefeld, R.M. 235 Bilal, B.A., see Baumann, M. 524 Billard, I. 470, 485, 495, 501–503, 506, 510 Billard, I., see Bouby, M. 474, 506 Billard, I., see Nehlig, A. 473, 474, 482, 485 Billard, I., see Rustenholtz, A. 474 Billard, I., see Simonin, J.P. 491 Billing, R. 489, 491 Billinge, S.J.L. 304 Billings, M., see Bell, J. 497 Bini, R., see Bungenstock, C. 521, 529, 533, 535 Binnemans, K., see Görller-Walrand, C. 369, 371, 376, 377, 380, 400, 520, 526, 556, 560, 561 Binnemans, K., see Mironov, V.S. 355, 366, 368–372 Biotteau, G. 325 Biotteau, G., see Hennion, M. 311 Biotteau, G., see Moussa, F. 324 Biradha, K., see Fujita, M. 355 Birch, D., see Billard, I. 470, 495, 501–503, 506 Birch, D.J.S., see Lopez, M. 489, 491, 500, 508 Birks, J. 467, 486 Bishop, A.R., see Louca, D. 263 Bishton, S.S. 547 Biswas, A., see Smolyaninova, V.N. 327 Björnsson, P. 268 Blacquère, R.J.H., see Cordfunke, E.H.P. 152, 207, 209 Blair, S. 509 Blanzat, B. 523, 524, 574 Blasco, J., see De Teresa, J.M. 298–300 Blasco, J., see Stankiewicz, J. 292 Blasco, J., see Subías, G. 323 Blasse, G. 483 Blau, W., see Holzer, W. 506 Bleaney, B. 357, 358, 365, 369, 371, 376 Bloch, D. 279, 281 Block, S., see Barnett, J.D. 522, 552, 554 Block, S., see Fujishiro, I. 519 Block, S., see Piermarini, G.J. 518, 519 Bloembergen, N. 356, 359, 360 Blonska, A., see Hennig, C. 215 Blount, E.I., see Vettier, C. 521, 535

Blume, M., see Murakami, Y. 263 Bocquet, B. 453, 455, 456 Bocquet, B., see Floquet, S. 453, 455–459 Bocquet, B., see Ouali, N. 379, 390, 405–410 Bodak, O., see Sologub, O. 41–43, 45, 46, 48, 49, 51–54, 56–63, 66–69, 72–76, 79–93, 102, 119–123, 133 Bodak, O.I., see Pankevich, Yu.V. 52, 59, 66, 73 Bodak, O.I., see Pecharsky, V.K. 40, 45, 52, 53, 59, 66, 67, 73, 79, 82, 84, 86, 88, 89, 92, 98, 100, 106, 109, 138, 139 Bodak, O.I., see Skolozdra, R.V. 41, 46, 53, 59, 60, 67, 73, 80, 82, 84, 86–88, 132, 133 Bodak, O.I., see Stetskiv, A.O. 55, 109, 111 Bodnar, R.E. 37 Boens, N., see Janssens, L.D. 471 Boens, N., see Molski, A. 489, 502 Bogacz, A., see Gaune-Escard, M. 151, 166–168, 179, 203–206, 222, 223 Boghosian, S. 184 Bogner, J., see Leithe-Jasper, A. 26 Bolduan, F. 522, 550, 566 Bolender, J.P., see Hopkins, T.A. 369, 377, 405, 410 Bolletta, F., see Sabbatini, N. 494 Bollore, G. 43, 47, 49, 50, 55, 57, 58, 60, 62, 69, 71, 72, 74, 75, 110 Bolton, J.R., see Mack, J. 474, 498 Bolton, J.R., see Wertz, J.E. 359, 364 Bombieri, G., see Aime, S. 420, 422 Bombieri, G., see Benetollo, F. 420 Bommer, H. 174, 210–215, 217–221 Bommer, H., see Hohmann, E. 210–214, 216, 218, 220, 222 Bonazzi, A., see Sabbatini, N. 494 Bonnenfant, A., see Bouby, M. 474 Booij, A.S., see Cordfunke, E.H.P. 181, 210, 211, 213, 218 Booij, A.S., see Furkaliouk, M.Y. 210 Booij, A.S., see Kovács, A. 228 Boonk, L., see Evers, C.B.H. 15, 23 Boonk, L., see Evers, Ch.B.H. 65, 71, 72, 74, 76, 77, 95 Borchers, J.A., see Erwin, R.W. 325 Borchers, J.A., see Huang, Q. 289, 325 Borchers, J.A., see Lynn, J.W. 299, 325 Borghs, G., see Gordon, I. 326 Borissevitch, I.E. 508 Börjesson, L., see Björnsson, P. 268 Borodulenko, G.P., see Korshunov, B.G. 204, 205 Borrrmann, H., see Gunselius, H. 151

AUTHOR INDEX Borsese, A. 36 Borsese, A., see Borzone, G. 36 Borshchevsky, A., see Caillat, T. 29 Borshchevsky, A., see Chen, B. 13 Borshchevsky, A., see Fleurial, J.-P. 3, 11, 13, 27, 29 Borshchevsky, A., see Watcharapasorn, A. 6, 7, 12, 13, 29 Borstel, G., see Slebarski, A. 45, 59, 60, 100, 113 Borzone, G. 36, 37, 135, 136 Borzone, G., see Borsese, A. 36 Borzone, G., see Cacciamani, G. 135 Borzone, G., see Ferro, R. 37, 135 Botta, M., see Aime, S. 357, 360–363, 420–422, 426, 429, 433, 439, 440 Botta, M., see Benetollo, F. 420 Botta, M., see Bruce, J.I. 355 Botta, M., see Marques, M.P.M. 421, 423 Bouby, M. 474, 506 Boulon, G., see Gaft, M. 480 Bouquet, F., see Fisher, R.A. 326 Bouquet, F., see Gordon, J.E. 326 Bourée, F., see André, G. 123 Bourée, F., see Autret, C. 338 Bourée, F., see Damay, F. 330, 336 Boutonnet, R., see Labeau, M. 203 Brachmann, A., see Geipel, G. 495, 499, 500, 505 Bradbury, M.I. 541 Bradley, D., see Holzer, W. 506 Bradley, J.A., see Wolford, D.J. 555 Brand, L., see Beechem, J.M. 498 Brand, L., see Laws, W.R. 498, 505 Braun, D., see Jeitschko, W. 2, 4, 6, 7, 15 Braun, D.J. 2, 4, 7, 11, 15, 44, 47, 49, 52, 56, 57, 59, 60, 62, 69, 71, 76–78 Braun, D.J., see Evers, C.B.H. 15, 23 Braun, D.J., see Evers, Ch.B.H. 65, 71, 72, 74, 76, 77, 95 Braun, D.J., see Grandjean, F. 8, 13, 23, 24 Bray, K.L. 517 Bray, K.L., see Culp, T.D. 524, 525, 578–580 Bray, K.L., see Lochhead, M.J. 471, 524, 555, 556, 581 Bray, K.L., see Shen, Y.R. 522, 525, 545, 564–566, 575–577 Bray, K.L., see Wamsley, P.R. 525, 575, 577 Bredig, M.A., see Dworkin, A.S. 151, 152, 166–168, 179–181, 200, 203–209, 222, 223 Breen, P.J. 473, 474 Brendler, V. 499 Brendler, V., see Bernhard, G. 495

595

Brendler, V., see Geipel, G. 495, 499, 500, 505 Brendler, V., see Rutsch, M. 501 Brese, N.E., see Gordon, R.A. 56, 95 Bretonnière, Y. 393 Brewer, L., see Lewis, G.N. 182 Briggs, J.M. 368, 455 Brina, R. 507 Brink, J.M. 364 Brinks, H.W. 275, 276 Brog, W.C., see Wood, V.E. 275 Bros, P., see Billard, I. 470, 495, 501–503, 506 Brosha, E.L., see Louca, D. 263 Brown, D. 152 Brown, D., see Fuger, J. 219, 220 Brown, D., see Hurtgen, C. 210, 212–214, 216, 218, 220 Brown, D.E., see Chmaissem, O. 278, 280 Brown, E., see Porter, B. 200, 201 Brown, J.M., see Bi, Q. 523, 529, 553 Bruce, J.I. 355 Bruce, J.I., see Aime, S. 426, 429 Bruce, J.I., see Clarkson, I.M. 484, 505 Brücher, E., see Sherry, A.D. 433 Brunelli, M., see Lanzara, A. 295, 325 Brunetti, B. 195, 236–240 Brunetti, B., see Piacente, V. 195, 237, 239, 240 Brunetti, B., see Villani, A.R. 195, 236, 238–240 Bruynseraede, Y., see Gordon, I. 326 Bryden, C.C. 376, 410, 471, 478, 505 Brylak, M. 42, 43, 48, 50, 56, 58, 61, 62, 69, 72, 75, 81, 83, 85, 87, 89, 90 Brylyak, M., see Wollesen, P. 43, 44, 46, 48, 49, 51, 52, 54, 57–61, 63, 66, 68, 70, 72, 73, 75, 80, 83 Bryzhina, M.F., see Yudin, V.M. 276 Buchanan, R.A., see Wickersheim, K.A. 567 Büchel, D. 151, 206 Bucher, J., see Allen, P. 474 Buchler, J.W. 449–453 Büchner, B., see Klingeler, R. 315 Büchner, B., see Uhlenbruch, S. 317 Buckau, G., see Monsallier, J.M. 506 Buddhudu, S. 484 Budhani, R.C., see Srivastava, S. 291, 292 Bud’ko, S.L., see Fisher, I.R. 90, 91, 134, 135, 137 Bukhtiyarov, V.V., see Korshunov, B.G. 204 Bukowski, Z., see Dabrowski, B. 311, 323 Bukowski, Z., see Xiong, X. 311 Bulou, A., see Wang, Q. 523, 533, 534 Bungenstock, C. 521, 529, 532–535, 537, 540–544, 546, 551

596

AUTHOR INDEX

Bunting, E.N., see Weir, C.E. 516 Bünzli, J.-C.G. 355, 366, 467, 471, 472, 493, 494, 496 Bünzli, J.-C.G., see Elhabiri, M. 443–445, 448, 481, 494 Bünzli, J.-C.G., see Floquet, S. 453, 455–459 Bünzli, J.-C.G., see Petoud, S. 355, 384–387 Bünzli, J.-C.G., see Piguet, C. 355, 384, 385, 393–395 Bünzli, J.-C.G., see Platas-Iglesias, C. 406, 407 Bünzli, J.-C.G., see Renaud, F. 387–393, 408 Bünzli, J.-C.G., see Rigault, S. 358, 366, 389, 390, 444, 446–448 Burdick, G.W. 548 Burdukovskaya, G.G., see Kudin, L.S. 193, 237, 238 Burgess, J. 221 Burgess, S., see Zhang, S. 355 Burgy, J. 332 Burkhard, W.J., see Corbett, J.D. 208 Burleigh, M.C., see Dai, S. 494 Burlet, P. 55 Burlet, P., see Rossat-Mignod, J. 55, 57 Burnashev, O.R., see Abdusalamova, M.N. 36, 37, 135 Burnett, J.L. 215 Burns, J.B., see Chen, G. 523, 557 Burns, P.D. 363 Burrows, H., see Billard, I. 470, 495, 501–503, 506 Burrows, H.D. 491, 492, 497 Burrows, H.D., see Azenha, M.E. 498 Burrows, H.D., see Miguel, M.G. 498 Burrows, H.D., see Rykov, S. 497 Burton, G.D., see Thoma, R.E. 201–203, 206, 207 Buschow, K.J., see Mentink, S.A.M. 54 Butera, A., see Causa, M.T. 326 Butman, M.F., see Kudin, L.S. 193, 237, 238 Buzare, J.Y., see Rewaj, T. 524, 536 Cacciamani, G. 135 Cacciamani, G., see Ferro, R. 37, 135 Cacciamani, G., see Riani, P. 93 Cacheris, W.P. 410 Cacheris, W.P., see Sherry, A.D. 433 Cader, M.S.R., see Greis, O. 149, 150, 166, 200–203 Cahill, J.A., see Kishenbaum, A.D. 178 Cai, W., see Zhao, Y.G. 328 Caillat, T. 29 Caillat, T., see Chen, B. 13 Caillat, T., see Fleurial, J.-P. 3, 11, 13, 27, 29

Caillat, T., see Nolas, G.S. 11 Caillat, T., see Watcharapasorn, A. 6, 7, 12, 13, 29 Calabi, L., see Bianchi, A. 426 Calvert, L.D., see Villars, P. 37 Camp, F.E., see Hirayama, C. 239, 240 Campbell, A.J. 319 Campbell, J.A., see Kennedy, R.J. 521, 522, 524, 525 Canedy, C.L., see Xiao, G. 328 Caneiro, A., see Allodi, G. 288 Caneiro, A., see Causa, M.T. 326 Canﬁeld, P.C., see Fisher, I.R. 90, 91, 134, 135, 137 Cantelli, R., see Cordero, F. 326 Cao, B.S., see Zhao, Y.G. 328 Cao, W.L., see Zhao, Y.G. 296 Capogna, L., see Radaelli, P.G. 329 Capozzi, F., see Bertini, I. 357, 361 Capponi, S., see Dagotto, E. 261 Caramagno, E., see Congeduti, A. 325 Carassiti, V., see Allsopp, S.R. 473, 474 Caravan, P. 357, 360–362 Cardona, M., see Trommer, R. 578 Cardoso, A.C., see Burrows, H.D. 497 Cardoso, A.C., see Miguel, M.G. 498 Carlson, G.L., see Hirayama, C. 196, 197, 239 Carnall, W.T. 160, 161, 383, 469, 471, 472, 481, 494 Casa, D. 315 Casa, D., see Kiryukin, V. 291 Casa, D., see Zimmermann, M.V. 264 Casado, J.A., see Berregi, I. 507 Castellano, C., see Cordero, F. 326 Castelli Guidi, M., see Allodi, G. 288 Castle, P.M., see Hirayama, C. 196, 197, 239, 240 Castro, M.M.C.A., see Sherry, A.D. 433 Causa, M.T. 326 Causa, M.T., see Rivadulla, F. 309, 321 Cava, R.J. 56 Cavalieri, S., see Bungenstock, C. 521, 529, 533, 535 Cerne, J., see Quijada, M.A. 296 Cesaro, S.N., see Bencze, L. 186, 226, 235 Cesaro, S.N., see Feltrin, A. 186, 191, 227–229, 231 Cestelli Guidi, M. 264 Ceulemans, A., see Mironov, V.S. 355, 366, 368–372 Chadi, D.J. 580 Chahara, K.I. 290 Chakoumakos, B.C. 8

AUTHOR INDEX Chakoumakos, B.C., see Dilley, N.R. 26 Chakoumakos, B.C., see Keppens, V. 11 Chakoumakos, B.C., see Sales, B.C. 7, 9–11, 13, 29, 31 Chaminade, J.-P., see Oppenländer, A. 522 Champagnon, B., see Gaft, M. 480 Chan, J.Y. 37, 90, 134 Chandran, R., see Forsberg, J.H. 357, 358, 374, 380, 427–431, 439, 440 Chang, C.-T.P., see Del Cul, G.D. 523 Chang, C.A. 420 Chang, C.A., see Holz, R.C. 478, 480, 502 Chang, C.W. 336 Chang, K.J., see Chadi, D.J. 580 Chang, N.C. 538 Chapados, C., see Max, J.J. 482 Chapon, D. 454, 455 Chapon, L., see Ravot, D. 10, 11, 13 Charlu, T.V. 164, 165 Charlu, T.V., see Besenbuch, G. 235 Charvillat, J.-P. 57, 61, 71, 75, 81 Chateau, C., see Lacam, A. 522, 529, 554 Chateau, C., see Leger, J.M. 522, 554 Chau, R., see Bauer, E.D. 13, 16 Chau, R., see Gajewski, D.A. 13 Chaudhuri, A.K., see Charlu, T.V. 164, 165 Chaussedent, S., see Monteil, A. 524, 556 Chauveau, F., see Mooney, W. 497 Chawla, S., see Sandhu, S. 497 Chechersky, V. 295, 296, 298, 305, 325 Chechersky, V., see Nath, A. 325 Cheetham, A.K., see Rao, C.N.R. 330 Chen, B. 13 Chen, B., see Morelli, D.T. 11 Chen, C.-C., see Lu, Q. 298 Chen, C.H. 328, 329 Chen, C.H., see Cheong, S.W. 323 Chen, C.H., see Mori, S. 328–330 Chen, C.H., see Uehara, M. 327 Chen, C.L., see Zhao, Y.G. 296 Chen, G. 522–524, 529, 549, 550, 557, 558 Chen, G., see Stump, N.A. 523, 557 Chen, H.J., see Zhang, J.S. 65, 73 Chen, J.W., see Torikachvili, M.S. 6, 8, 17, 22 Chen, L., see Tang, X. 29, 30 Chen, W., see Franck, J.P. 307 Chen, Y.-R. 285 Chen, Z., see Saraf, L.V. 309 Cheong, S.-W., see Chen, C.H. 328, 329 Cheong, S.-W., see Cox, D.E. 291 Cheong, S.-W., see Fernández-Baca, J.A. 321

597

Cheong, S.-W., see Granado, E. 329 Cheong, S.-W., see Heffner, R.H. 298, 325 Cheong, S.-W., see Hwang, H.Y. 290, 291 Cheong, S.-W., see Kim, K.H. 327, 328 Cheong, S.-W., see Lanzara, A. 295, 325 Cheong, S.-W., see Liu, H.L. 328 Cheong, S.-W., see Mori, S. 328–330 Cheong, S.-W., see Naler, S. 328 Cheong, S.-W., see Podzorov, V. 327 Cheong, S.-W., see Radaelli, P.G. 299, 323, 325, 327, 329 Cheong, S.-W., see Schiffer, P. 328 Cheong, S.-W., see Uehara, M. 323, 327–329, 340 Cheong, S.-W., see Yoon, S. 326 Cheong, S.-W., see Yoshinari, Y. 328 Cheong, S.W. 323 Chernogorenko, V.B., see Kobzenko, G.F. 36 Chi, Y. 523, 524, 530, 533, 534, 536, 539 Chi, Y., see Liu, S. 523, 524, 529, 530, 533, 539 Chi, Y., see Wang, L. 523, 524, 551, 568 Chi, Y., see Wang, Q. 524, 530, 538 Chistotina, E.A., see Babushkina, N.A. 308, 309 Chmaissem, O. 278, 280 Chmaissem, O., see Dabrowski, B. 311, 323 Chmaissem, O., see Xiong, X. 311 Choi, E.J., see Jung, J.H. 323 Choi, J.-W., see McIlroy, D.N. 295 Choppin, G.R. 387, 467, 493, 495, 499, 505 Choppin, G.R., see Barthelemy, P.P. 478, 479 Choppin, G.R., see Billard, I. 470, 495, 501–503, 506 Choppin, G.R., see Bünzli, J.-C.G. 467, 471, 472, 493, 496 Choppin, G.R., see De Sa, G.F. 471, 483 Choppin, G.R., see Hasegawa, Y. 479, 480 Choppin, G.R., see Kimura, T. 473, 478, 479, 481 Choppin, G.R., see Lis, S. 471, 473, 478–481, 494, 496 Choppin, G.R., see Shin, H. 478 Choppin, G.R., see Wang, Z.M. 478, 494, 495, 499, 505 Chouteau, G., see Dupont, F. 336 Chouteau, G., see Millange, F. 336 Chrétien, A., see De Kozak, A. 201 Christensen, A.L., see King, E.G. 154, 164, 176, 178, 200 Chrzanowski, J., see Franck, J.P. 307 Chu, C.W., see Alexandrov, A.S. 308 Chudinovskikh, L., see Shen, Y.R. 564 Chuiko, A.G., see Abdusalamova, M.N. 37 Chuiko, A.G., see Abulkhaev, V.D. 94

598

AUTHOR INDEX

Chun, S.H. 298 Churchill, M.R., see Amin, S. 426 Churchill, M.R., see Morrow, J.R. 426 Ciach, S. 236, 237 Ciano, M., see Sabbatini, N. 494 Clarkson, I., see Beeby, A. 481–484 Clarkson, I.M. 484, 505 Clementi, V. 359 Cohen, L.F., see Freitas, R.S. 310 Cohn, J.L., see Neumeier, J.J. 283 Cohn, J.L., see Nolas, G.S. 11 Coldea, R., see Keppens, V. 11 Collings, E.W., see Wood, V.E. 275 Conder, K., see Zhao, G.-M. 305, 307 Congeduti, A. 325 Cooper, S.L., see Liu, H.L. 328 Cooper, S.L., see Naler, S. 328 Cooper, S.L., see Yoon, S. 326 Corbett, J.D. 5, 208, 209 Corbett, J.D., see Druding, L.F. 204, 208 Corbett, J.D., see Ganguli, A.K. 42, 110 Corbett, J.D., see Guloy, A.M. 49 Corbett, J.D., see Mee, J.E. 208 Cordero, F. 326 Cordfunke, E.H.P. 152, 171, 172, 174, 181, 207–211, 213, 218, 220, 221 Cordfunke, E.H.P., see Furkaliouk, M.Y. 210, 211, 220, 222 Cordfunke, E.H.P., see Van Roosmalen, J.A.M. 267 Cordier, G. 43, 44, 46 Cordier, G., see Sologub, O. 43, 46, 47, 51, 54, 60, 68, 74, 103 Cornelius, A.L., see Neumeier, J.J. 278 Corradi, G., see Dierolf, V. 525, 529, 555 Corsi, D.M. 356 Cortes, R., see Grandjean, F. 13 Cousseins, J.C., see Labeau, M. 203 Couston, L. 499 Couston, L., see Billard, I. 470, 495, 501–503, 506 Couston, L., see Moulin, C. 508 Cox, A., see Allsopp, S.R. 473, 474 Cox, D.E. 291 Cox, D.E., see Radaelli, P.G. 327, 329 Cox, J.D. 173 Craig, I., see Allen, P. 474 Credi, A., see Balzani, V. 355 Crich, S.G., see Aime, S. 433 Cripe, D.M., see Robinson, M. 200 Crosswhite, H., see Dieke, G.H. 154, 160 Crosswhite, H.M., see Dieke, G.H. 154, 160

Cui, H., see Guo, C. 524, 539 Culp, T.D. 524, 525, 578–580 Cundari, T.R. 148, 185, 189 Cunningham, B.B., see Burnett, J.L. 215 Cunningham, B.B., see Lohr, H.R. 210, 212 Cunningham, J. 489, 497 Curtis, M.M. 544 Daane, A.H., see Spedding, F.H. 149, 200–209 Dabrowski, B. 311, 323 Dabrowski, B., see Chmaissem, O. 278, 280 Dabrowski, B., see Xiong, X. 311 Dadgar, A., see Choppin, G.R. 499 Dagotto, E. 261 Dagotto, E., see Burgy, J. 332 Dai, P. 325 Dai, P., see Fernández-Baca, J.A. 321 Dai, P., see Keppens, V. 11 Dai, S. 494 Daire, M. 215 Dalichaouch, Y., see Torikachvili, M.S. 6, 8, 17, 22 Damay, F. 330, 336 Damay, F., see Freitas, R.S. 310 Damien, D., see Charvillat, J.-P. 57, 61, 71, 75, 81 d’Amour-Sturm, H., see Gregorian, T. 521, 529, 531, 532, 536, 537, 540, 541, 545, 559 Daniel, J.F. 151, 205 Dannebrock, M.E. 10, 21, 23, 24 Daoud-Aladine, A., see Pinsard-Gaudart, L. 268, 280 Daoud-Aladine, M. 328, 335, 336 Daramagnyan, A.P., see Azenha, M.E. 498 Darling, T.W., see Dilley, N.R. 26 Dartyge, E., see Tolentino, H. 518 Das, A., see Gordon, I. 326 Das, A., see Vijaya Lakshmi, K. 121, 124 Dass, R.I., see Goodenough, J.B. 272–274 Datchi, F. 522, 554 Davis, R.E., see Wilcott, M.R. 373, 385 de Blas, A., see Geraldes, C.F.G.C. 358, 378, 404, 405 de Blas, A., see Platas, C. 358, 359, 377, 378, 400–404 de Brion, S., see Dupont, F. 336 De Brion, S., see Millange, F. 336 De Cian, A., see Moussavi, M. 440 De Cillis, F.M., see Sacco, A. 482 de Gennes, P.-G. 258 De Kozak, A. 201, 202 de Leon-Guevara, A.M., see Vasiliu-Doloc, L. 299, 318

AUTHOR INDEX de Lozanne, A., see Lu, Q. 298 De Renzi, R., see Allodi, G. 288, 325, 328, 337 De Renzi, R., see Cestelli Guidi, M. 264 De Sa, G.F. 471, 483 De Schryver, F.C., see Janssens, L.D. 471 de Sousa, A., see Beeby, A. 481–484 de Sousa, A.S., see Aime, S. 426, 429 de Sousa, A.S., see Dickins, R.S. 482 De Teresa, J.M. 298–300 De Teresa, J.M., see García-Landa, B. 338 Deakin, L. 133 Debnath, A.K., see Chang, C.W. 336 Decambox, P. 507, 508 Decambox, P., see Berthoud, T. 507, 508 Decambox, P., see Couston, L. 499 Decambox, P., see Moulin, C. 507, 508 Decambox, P., see Thouvenot, P. 507 deCian, A.D., see Buchler, J.W. 449, 450 Dedieu, A., see Berny, F. 358 Dediu, V. 327 DeGraff, B.A., see Bare, W.D. 470, 509 DeKock, C.W., see Lesiecki, M. 186, 224 DeKock, C.W., see Wesley, R.D. 186, 191, 224, 225 Del Cul, G.D. 523, 558 del Moral, A., see De Teresa, J.M. 298, 299 Delacote, D., see Rossat-Mignod, J. 55, 57 Delaney, R.M., see Forsberg, J.H. 357, 358, 374, 380, 427–431, 439, 440 Delangle, P., see Chapon, D. 454, 455 Delaplane, R.G., see Wasse, J.C. 179 Delﬁno, S., see Borzone, G. 36 Deline, T.A. 161, 163 Dellonte, S., see Sabbatini, N. 494 Delong, L.E. 6, 8, 9 Demas, J.N., see Bare, W.D. 470, 509 Demas, J.N., see Metcalf, D.H. 489 Demas, J.N., see Sharman, K.S. 470 DeMattei, R.C., see Watcharapasorn, A. 6, 12, 13, 29 Dender, D.C., see Huang, Q. 328, 329 Denis, J.P., see Blanzat, B. 523, 524, 574 Denning, R. 557 Deschaux, M. 498 Deschaux, M., see Marcantonatos, M.D. 497 Desreux, J.F. 357, 421, 422 Desreux, J.F., see Bryden, C.C. 410 Desreux, J.F., see Jacques, V. 423 Desreux, J.F., see Reilley, C.N. 357, 376, 377, 404–407, 410, 443 Desreux, J.F., see Spirlet, M.-R. 420

599

Dessau, D.S. 268 Dettingmeijer, J.H. 196, 240 Deventer, E.V., see Rudzitis, E. 215, 219 Devlin, E., see Kallias, G. 328 Devlin, E., see Simopoulos, A. 328 Dewalsky, M.V., see Jeitschko, W. 15, 23, 24 Dewey, H.J. 467 Dewhurst, C.D., see Lees, M.R. 291 Dexter, D.L. 569–571 Dho, J. 322, 325, 328 Di Bella, S. 185 Dias, F., see Freitas, R.S. 310 Dickey, R.P., see Bauer, E.D. 8, 12, 15, 17 Dickins, R., see Beeby, A. 481–484 Dickins, R.S. 481, 482 Dickins, R.S., see Bruce, J.I. 355 Dieke, G.H. 154, 160, 552 Dielis, H.R., see Dettingmeijer, J.H. 196, 240 Dierolf, V. 525, 529, 555 Dietrich, L., see Wollesen, P. 43, 44, 46, 48, 49, 51, 52, 54, 57–61, 63, 66, 68, 70, 72, 73, 75, 80, 83 Dikovsky, V., see Yuzhelevski, Y. 326 Dilley, N.R. 15, 26 Dilley, N.R., see Bauer, E.D. 8, 12, 13, 15–17 Dilley, N.R., see Dordevic, S.V. 8, 12, 17, 26, 27 Dilley, N.R., see Gajewski, D.A. 13 Dimitropoulos, C., see Papavassiliou, G. 325, 326, 328 Dimmock, J.O., see Oliver, M.R. 252 DiSalvo, F.J., see Gordon, R.A. 56, 95, 97, 100, 113 Dlouhá, M., see Jirák, Z. 275, 291 Dmowski, W., see Louca, D. 304 Dobson, C.M., see Bleaney, B. 357, 365, 371 Dogotto, E., see Mayr, M. 326 Dolg, M. 148, 183, 187–189 Dolinsek, C., see Papavassiliou, G. 325 Dolinsek, J., see Papavassiliou, G. 328 Donato, H. 404 Donni, A., see Keller, L. 17, 23 Dordevic, S., see Dilley, N.R. 26 Dordevic, S.V. 8, 12, 17, 26, 27 Dorfman, R.C., see Morrison, M.E. 489 Doumerc, J.-P., see Töpfer, J. 286, 287, 289 Dow, J.D., see Ren, S.Y. 580 Dowben, P.A., see McIlroy, D.N. 295 Drew, H.D., see Quijada, M.A. 269, 296 Drew, H.D., see Romero, D.B. 268 Drew, H.D., see Zhao, Y.G. 296 Drickamer, H.G., see Drotning, W.D. 521, 524, 550

600

AUTHOR INDEX

Drickamer, H.G., see Fitch, R.A. 516 Drickamer, H.G., see Hayes, A.V. 522–524, 571, 572 Drickamer, H.G., see Keating, K.B. 521–525, 562 Drickamer, H.G., see Tyner, C.E. 523, 550 Drickamer, H.G., see Wang, P.J. 522–525, 550 Drickamer, H.G., see Webster, G.A. 524, 551, 567, 568, 574 Drobot, D.V., see Korshunov, B.G. 204, 205 Drobot, D.V., see Pashinkin, A.S. 237 Drost, R., see García-Landa, B. 338 Drotning, W.D. 521, 524, 550 Druding, L.F. 204, 208 Druding, L.F., see Corbett, J.D. 208 Du, Y.-W., see Li, J.-M. 325 Dubois, V., see Billard, I. 470, 495, 501–503, 506 Dubost, J.P. 420 Dudareva, A.G., see Molodkin, A.K. 208 Dudchik, G.P. 236–238 Dudchik, G.P., see Makhmadmurodov, A. 195, 239 Dudek, H. 206 Dudkin, L.D. 29 Dunner, J. 77, 95 Dupas, C., see Anane, A. 291 Duplâtre, G., see Rustenholtz, A. 474 Dupont, F. 336 Durand, J.S., see Berregi, I. 507 Dwight, A.E. 37, 40–42, 72, 76, 79, 81–90, 92, 93 Dwight, A.E., see Shaked, H. 84, 87, 89, 90, 127, 129 Dworkin, A.S. 151, 152, 166–168, 179–181, 200, 203–209, 222, 223 Dyakonov, K., see Ilisavskii, Y. 326 Dyakonov, V.P., see Ilisavskii, Y. 326 D’yakov, Y.A., see Berezhkovskii, A.M. 489 Dybzinski, R., see Dabrowski, B. 311, 323 Dybzinski, R., see Xiong, X. 311 Dzialoshinskii, I.E. 258 Earl, W.L., see Pinkerton, A.A. 415–418 Ebel, T., see Albering, J.H. 76, 90 Ebel, T., see Evers, C.B.H. 15, 23 Ebel, T., see Evers, Ch.B.H. 65, 71, 72, 74, 76, 77, 95 Edder, C., see Piguet, C. 355, 393 Edelstein, N., see Allen, P. 474 Edelstein, N.M., see Yoo, C.S. 522, 549, 550 Edvalson, J.H., see Hornbostel, M.D. 8 Effantin, J.M., see Rossat-Mignod, J. 55, 57 Eﬁmov, M.E., see Furkaliouk, M.Y. 216 Egami, T. 261, 263, 292, 304

Egami, T., see Louca, D. 263, 304 Ehlers, G., see Heffner, R.H. 298 Ehrlich, A.C., see Nolas, G.S. 11 Ehrlich, S., see Oppermann, H. 210 Eichhorn, M. 569 Eick, H.A., see Biefeld, R.M. 235 Einarsrud, M.A., see Faaland, S. 323 El Azzi, A., see Billard, I. 510 El-Ansi, T.A., see Choppin, G.R. 499 Elbanowski, M., see Hnatejko, Z. 482, 496 Elgavish, G.A., see Reuben, J. 365, 376, 379, 380 Elhabiri, M. 443–445, 448, 481, 494 Elhabiri, M., see Nehlig, A. 473, 474, 482, 485 Eliet, V. 474, 498, 501 Eliseev, A.A., see Abdusalamova, M.N. 37 Ellenwood, R.E., see Ferguson, M.J. 48, 57, 61, 70, 102 Ellison, J.J., see Caravan, P. 357, 360–362 Elzinga, G.D., see Cordfunke, E.H.P. 152, 207, 208 Emin, D. 293 Endoh, Y. 315 Endoh, Y., see Martin, M.C. 322 Endoh, Y., see Murakami, Y. 263 Endoh, Y., see Nojiri, H. 317 Englisch, U., see Shen, Y.R. 564 Eremets, M. 517, 519, 561 Ericksson, S., see Björnsson, P. 268 Eriksen, J., see Björnsson, P. 268 Ermolaev, V.L. 495, 497, 499, 501, 503 Ermondi, G., see Aime, S. 357, 361, 363, 421, 422, 439, 440 Erwin, R.W. 325 Erwin, R.W., see Huang, Q. 289, 325, 328, 329 Erwin, R.W., see Lynn, J.W. 299, 325 Evans, D.F. 356 Evers, C.B.H. 15, 23 Evers, C.B.H., see Dannebrock, M.E. 10, 21, 23, 24 Evers, C.B.H., see Jeitschko, W. 15, 23, 24 Evers, Ch.B.H. 65, 71, 72, 74, 76, 77, 95 Evseeva, G.V. 236 Exarhos, G.J., see Hess, N.J. 523, 553, 554 Eyring, L., see Machlan, G.R. 214, 215, 221 Ezhov, Y.S. 230 Faaland, S. 323 Fahey, J.A., see Morss, L.R. 214, 218 Fanghänel, T. 495, 496, 500 Fanghänel, T., see Aas, W. 500

AUTHOR INDEX Fanghänel, T., see Billard, I. 470, 495, 501–503, 506 Fanghänel, T., see Paviet, P. 500 Fanghänel, T., see Stumpf, T. 495 Farber, G.K., see Albin, M. 478, 499, 505 Fardis, M., see Papavassiliou, G. 325, 326, 328 Fasano, M., see Aime, S. 357, 360, 362, 420–422 Faslyeva, N.D., see Abdusalamova, M.N. 37 Fäth, M. 298 Faucher, M., see Garcia, D. 542, 550 Faucher, M.D. 550 Faulkner, S., see Beeby, A. 481–484 Fazakerley, G.V., see Evans, D.F. 356 Fazekas, Z., see Yamamura, T. 491, 492 Fazlyeva, N.D., see Abdusalamova, M.N. 36, 37 Fedorov, P.P., see Sobolev, B.P. 150, 200–203 Feigelson, R.S., see Watcharapasorn, A. 6, 7, 12, 13, 29 Feiguin, A., see Mayr, M. 326 Feldman, J.L. 11 Felmy, A.R. 506 Felner, I., see Markovich, V. 287 Feltrin, A. 186, 191, 227–229, 231 Feltrin, A., see Bencze, L. 186, 226, 235 Feng, D., see Li, J.-M. 325 Ferdeghini, C., see Dediu, V. 327 Ferguson, M.J. 43, 47–50, 57, 58, 61–63, 70, 72, 75, 79, 82, 84, 102, 103 Ferguson, M.J., see Bollore, G. 43, 47, 49, 50, 55, 57, 58, 60, 62, 69, 71, 72, 74, 75, 110 Ferguson, M.J., see Raju, N.P. 43 Fernández-Baca, J.A. 321 Fernandez-Baca, J.A., see Dai, P. 325 Fernandez-Baca, J.A., see Yamada, Y. 315 Fernández-Díaz, M.T. 329 Fernández-Díaz, M.T., see Daoud-Aladine, M. 328, 335, 336 Ferrari, M., see Monteil, A. 524, 556 Ferretti, M., see Cordero, F. 326 Ferro, R. 37, 135 Ferro, R., see Borsese, A. 36 Ferro, R., see Borzone, G. 36, 37, 135, 136 Ferro, R., see Cacciamani, G. 135 Ferro, R., see Flandorfer, H. 91, 92, 118 Ferro, R., see Marazza, R. 41, 48, 56, 61, 69, 74, 81, 83, 85, 87, 88, 91, 106 Ferro, R., see Riani, P. 41, 85, 87, 88, 91, 93 Ferro, R., see Rossi, D. 49, 57, 71, 76 Feuersanger, A.E., see Struck, C.W. 196, 239, 240 Ficalora, P., see Hastie, J.W. 193, 197, 236, 237 Fiebig, M. 291

601

Fiebig, M.K. 291 Field, L.D., see Baker, M.V. 356 Fields, P.R., see Carnall, W.T. 494 Finger, L.W., see Hazen, R.M. 518 Fini, L., see Bungenstock, C. 521, 533 Fink, H., see Seifert, H.J. 203, 204 Finkelshtein, L.D., see Aliev, O.M. 77, 78, 91 Fischer, H.O. 49, 58, 62 Fischer, J., see Buchler, J.W. 449, 450 Fischer, J., see Moussavi, M. 440 Fischer, K., see Zimmer, H.G. 523 Fischer, P., see Keller, L. 17, 23 Fisher, I.R. 90, 91, 134, 135, 137 Fisher, R.A. 326 Fisher, R.A., see Gordon, J.E. 326 Fisk, Z., see Yoon, S. 326 Fita, I., see Markovich, V. 325 Fitch, R.A. 516 Fitzgibbon, G.C. 210, 212, 215–217 Fitzgibbon, G.C., see Baker, F.B. 214 Fitzgibbon, G.C., see Huber Jr., E.J. 218 Fjellvåg, H., see Brinks, H.W. 275, 276 Flandorfer, H. 91, 92, 118, 127 Fletcher, S., see Brown, D. 152 Fleurial, J.-P. 3, 11, 13, 27, 29 Fleurial, J.-P., see Caillat, T. 29 Fleurial, J.-P., see Chen, B. 13 Fleurial, J.-P., see Watcharapasorn, A. 6, 7, 12, 13, 29 Floquet, S. 453, 455–459 Floquet, S., see Bocquet, B. 453, 455, 456 Flotow, H.E. 154, 157 Flotow, H.E., see Lyon, W.G. 154, 157, 162–164, 166 Flynn, J.P., see Spedding, F.H. 210–212, 215, 216, 219 Foecker, A.J., see Jeitschko, W. 15, 23, 24 Folcher, G., see Arvis, M. 497 Folcher, G., see Mooney, W. 497 Fondado, A., see Mira, J. 295 Fondado, A., see Rivadulla, F. 309 Fonger, W.H. 523, 524, 567 Fonger, W.H., see Struck, C.W. 567, 568, 572 Fontaine, A., see Tolentino, H. 518 Fontcuberta, J. 299 Fontcuberta, J., see García-Muñoz, J.L. 323 Fontcuberta, J., see Laukhin, V. 299 Fontcuberta, J., see Martínez, B. 317 Fontcuberta, J., see Senis, R. 317 Fontcuberta, J., see Skumryev, V. 312 Foong, F., see McIlroy, D.N. 295

602

AUTHOR INDEX

Forman, R.A., see Piermarini, G.J. 518 Formosinho, S., see Rykov, S. 497 Formosinho, S.J., see Azenha, M.E. 498 Formosinho, S.J., see Burrows, H.D. 497 Formosinho, S.J., see Miguel, M.G. 498 Fornasini, M.L., see Borzone, G. 37, 135, 136 Fornasini, M.L., see Merlo, F. 91, 92 Forsberg, J.H. 357, 358, 364, 367, 368, 371–374, 380, 427–431, 439, 440 Förster, T. 483, 569, 570 Fort, D., see Thornton, M.J. 124 Fournier, P., see Smolyaninova, V.N. 327 Fragalá, I., see Di Bella, S. 185 Fragalá, I.L., see Lanza, G. 189 Francesconi, L.C., see Chang, C.A. 420 Francisco, J., see Steinfeld, J. 487 Franck, J.P. 307 Franck, J.P., see Chechersky, V. 295, 296, 305, 325 Franck, J.P., see Fisher, R.A. 326 Franck, J.P., see Gordon, J.E. 326 Franklin, S.J., see Wu, S.L. 492 Franzen, H.F., see Mozharivskyj, Yu. 37, 41, 42, 80, 81, 83, 85, 87–90, 93 Franzen, H.F., see Zeng, L. 48 Fraternali, F. 358 Fraternali, F., see Ulrich, G. 358 Frederick, N.A., see Bauer, E.D. 21, 22 Frederick, N.A., see Maple, M.B. 22 Freeman, A.J. 377 Freeman, E.J., see Bauer, E.D. 8, 12, 15, 17, 24 Freeman, E.J., see Dilley, N.R. 15, 26 Freeman, E.J., see Gajewski, D.A. 13 Freeman, E.J., see Keppens, V. 11 Freibert, F., see Dilley, N.R. 26 Freisem, S., see Fäth, M. 298 Freitas, R.S. 310, 328, 329 Freitas, R.S., see Levy, P. 328 Frey, S.T. 496 Frick, B. 94, 140 Friedt, O., see Uhlenbruch, S. 317 Frimmel, F.H., see Monsallier, J.M. 506 Fronczek, F. 381 Frontera, C. 336 Frontera, C., see Llobet, A. 336 Frullano, L. 421 Fu, P.K.L. 355 Fuger, J. 171, 219, 220, 500 Fuger, J., see Bettonville, S. 217, 219, 221 Fuger, J., see Hurtgen, C. 210, 212–214, 216, 218, 220

Fuger, J., see Merli, L. 174, 210, 213, 216, 220–222 Fuger, J., see Morss, L.R. 467 Fujishiro, H. 276, 322, 326 Fujishiro, I. 519 Fujita, M. 355 Fujita, N., see Fujita, M. 355 Fukase, T., see Fujishiro, H. 326 Fukuda, T., see Endoh, Y. 315 Fukushima, K., see Iwadate, Y. 179 Fulde, P., see Thalmeier, P. 582 Furkaliouk, M.Y. 210, 211, 216, 217, 220–222 Furkaliouk, M.Y., see Cordfunke, E.H.P. 213, 218 Furkalyuk, M.Y., see Leonidov, V.Y. 218 Furrer, A., see Mesot, J. 524, 535 Furukawa, N., see Dagotto, E. 261 Furukawa, Y., see Yakubovskii, A. 309 Fusi, V., see Bazzicalupi, C. 492, 509 Gaft, M. 480 Gagliardi, L., see Spencer, S. 493 Gaillard, C., see Billard, I. 510 Gajewski, D.A. 13 Gajewski, D.A., see Keppens, V. 11 Galas, O., see Bertini, I. 363 Galatanu, A., see Bauer, E. 24 Galchenko, I.E., see Korshunov, B.G. 204, 205 Galli, M., see Bauer, E. 24 Galyametdinov, Y.G., see Mironov, V.S. 355, 366, 368–372 Gamanovich, N.M. 219 Gambino, R.J. 94 Gamelin, D.R. 355 Gampe, T., see Stangret, J. 482 Ganguli, A.K. 42, 110 Ganzyuk, A.L., see Skolozdra, R.V. 41, 46, 53, 59, 60, 67, 73, 80, 82, 84, 86–88, 132, 133 Gao, C., see Liu, S. 524, 539 García, A., see Granado, E. 284, 329 Garcia, D. 542, 550 García, J., see De Teresa, J.M. 298–300 García, J., see Stankiewicz, J. 292 García, J., see Subías, G. 323 García-Landa, B. 338 García-Muñoz, J.L. 323 García-Muñoz, J.L., see Frontera, C. 336 García-Muñoz, J.L., see Laukhin, V. 299 García-Muñoz, J.L., see Llobet, A. 336 Gardner, J.S., see Heffner, R.H. 298 Gardner, J.S., see Wiebe, C.R. 282 Gardner, P.J. 168 Garton, G. 205

AUTHOR INDEX Garvin, D., see Parker, V.B. 173 Gatteschi, D., see Hedinger, R. 454 Gaune-Escard, M. 151, 166–168, 179, 203–206, 222, 223 Gaune-Escard, M., see Rycerz, L. 166, 168, 179, 180, 204–206, 222, 223 Gavrichev, K.S. 161, 163 Gavrichev, K.S., see Gorbunov, V.E. 157, 158, 160 Gavrichev, K.S., see Tolmach, P.I. 157, 158, 160 Gavrilishina, A.I., see Yudin, V.M. 276 Geballe, T.H., see Worledge, W.C. 323 Geck, J., see Klingeler, R. 315 Geertsma, W. 277 Geidarova, E.A. 42, 71, 75, 85 Geidarova, E.A., see Rustamov, P.G. 81, 83 Geidarova, E.A., see Sadygov, F.M. 75 Geipel, G. 495, 499, 500, 505 Geipel, G., see Bernhard, G. 495 Geipel, G., see Billard, I. 470, 495, 501–503, 506 Geipel, G., see Brendler, V. 499 Geipel, G., see Rutsch, M. 501 Georges, J. 495, 508 Geraldes, C.F.G.C. 357, 358, 378, 404, 405, 410, 411, 414, 415, 417, 418, 420, 424, 425, 427, 429–433, 435–440, 442, 443, 451, 453 Geraldes, C.F.G.C., see Aime, S. 421, 422 Geraldes, C.F.G.C., see Frullano, L. 421 Geraldes, C.F.G.C., see Marques, M.P.M. 421, 423 Geraldes, C.F.G.C., see Platas, C. 358, 359, 377, 378, 400–404 Geraldes, C.F.G.C., see Ren, J. 420, 423–426, 429, 431, 433–435, 437–440 Geraldes, C.F.G.C., see Sherry, A.D. 357, 377, 411–413, 433 Gerard, A., see Grandjean, F. 8, 13, 23, 24 Gerloch, M. 368 Gershenson, M.E., see Podzorov, V. 327 Gershikov, A.G., see Spiridonov, V.P. 227 Geurts, F.A.J., see Klink, S.I. 471, 494–496 Geydarova, E.N. 85 Ghisletta, M., see Hedinger, R. 454 Ghivelder, L., see Freitas, R.S. 310, 328, 329 Ghivelder, L., see Levy, P. 328 Ghosh, B., see Mandal, P. 312 Ghosh, K., see Chechersky, V. 295, 296, 298, 305, 325 Ghosh, K., see Huang, Q. 325, 328, 329 Ghosh, K., see Malik, S.R. 95 Ghosh, K., see Smolyaninova, V.N. 329 Ghosh, K., see Zhao, G. 329 Giannotti, C., see Mooney, W. 497

603

Gibbs, D., see Murakami, Y. 263 Gibbs, D., see Zimmermann, M.V. 264 Gibson, J.K. 192, 234 Giefers, H., see Bungenstock, C. 540 Gierlowski, P., see Ilisavskii, Y. 326 Gietmann, C. 194, 196, 197, 207, 209, 238–240 Gil, A.M.P.C., see Burrows, H.D. 497 Gill, D., see Meiboom, S. 363 Ginley, D.S., see Schirber, J.E. 521 Giorgi, C., see Bazzicalupi, C. 492, 509 Giorgi, C., see Bianchi, A. 426 Girichev, G.V. 227–229 Girichev, G.V., see Giricheva, N.I. 184, 186, 190, 191, 193, 227–229, 232 Girichev, G.V., see Zakharov, A.V. 184, 186, 190, 191, 195, 229, 232 Giricheva, N.I. 184, 186, 190, 191, 193, 227–229, 232 Giricheva, N.I., see Girichev, G.V. 229 Giricheva, N.I., see Zakharov, A.V. 184, 186, 190, 191, 195, 229, 232 Giroux, S. 494, 505 Gladrow, E., see Beck, H.P. 558, 559 Glasel, J.A., see Barry, C.D. 363 Gleason, J.K. 524, 551, 566, 568 Gliemann, G., see Yersin, H. 523, 569 Glybin, V.P., see Gamanovich, N.M. 219 Godart, C., see Flandorfer, H. 91, 92, 118, 127 Godart, C., see Leithe-Jasper, A. 26 Godart, C., see Patil, S. 53, 80, 133 Godfrey, R.P., see Saraf, L.V. 309 Godzaev, E.M., see Rustamov, P.G. 77 Goffart, J., see Tröster, Th. 531–533, 536, 542, 543 Gog, Th., see Zimmermann, M.V. 264 Gogadze, N.G. 201–203 Golding, R.M. 357, 360, 365, 366, 371, 372 Goldschmidt, Z.B. 526, 530 Goldsmid, H.J. 28, 29 Goldsmid, H.J., see Nolas, G.S. 28 Goltsev, A., see Ilisavskii, Y. 326 Golushina, L.N., see Gavrichev, K.S. 161, 163 Golushina, L.N., see Tolmach, P.I. 157, 158, 160 Goncharenko, I., see Pinsard-Gaudart, L. 268, 280 Goncharov, A.F. 522, 582 Gong, G.Q., see Xiao, G. 328 Gonzalez, J. 518 González-Calbet, J.M., see Alonso, J. 324 Good, B.W., see Reilley, C.N. 357, 376, 377, 404–407, 410, 443

604

AUTHOR INDEX

Goodenough, J.B. 250, 251, 256, 261–263, 265, 267, 269, 270, 272–274, 277, 282, 293, 296, 298, 326, 327, 332 Goodenough, J.B., see Archibald, W. 294, 295, 300 Goodenough, J.B., see Liu, G.-L. 311, 313, 316, 318 Goodenough, J.B., see Overend, N. 303 Goodenough, J.B., see Rivadulla, F. 328, 330–335, 337–342 Goodenough, J.B., see Tichy, R.S. 277 Goodenough, J.B., see Töpfer, J. 269, 286, 288, 289 Goodenough, J.B., see Zhou, J.-S. 264, 265, 268, 269, 271, 272, 276–282, 284, 300–302, 305–308, 311, 312, 316, 317, 319–322 Goodman, G.L., see Carnall, W.T. 383 Gopalakrishnan, J., see Zhao, Y.G. 328 Gopich, I.V., see Agmon, N. 489 Gorbenko, O., see Shames, A.I. 338 Gorbenko, O., see Yakubovskii, A. 309 Gorbenko, O.Yu., see Babushkina, N.A. 308, 309, 327 Gorbunov, V.E. 157, 158, 160 Gorbunov, V.E., see Gavrichev, K.S. 161, 163 Gorbunov, V.E., see Tolmach, P.I. 157, 158, 160 Gordon, I. 326 Gordon, J.E. 326 Gordon, J.E., see Fisher, R.A. 326 Gordon, R.A. 56, 95, 97, 100, 113 Görller-Walrand, C. 369, 371, 376, 377, 380, 400, 520, 526, 556, 560, 561 Görller-Walrand, C., see Mironov, V.S. 355, 368–372 Gorodetsky, G., see Markovich, V. 287, 325 Gorodetsky, G., see Yuzhelevski, Y. 326 Gorodetsky, P., see Loa, I. 268 Goryushkin, V.F. 180, 182, 205, 206, 209, 223 Goryushkin, V.F., see Furkaliouk, M.Y. 216, 217, 220, 221 Goryushkin, V.F., see Gavrichev, K.S. 161, 163 Goryushkin, V.F., see Gorbunov, V.E. 157, 158, 160 Goryushkin, V.F., see Kiseleva, T.V. 204 Goryushkin, V.F., see Laptev, D.M. 203, 204 Goryushkin, V.F., see Monaenkova, A.S. 218 Goryushkin, V.F., see Pogrebnoi, A.M. 193, 194, 236, 237 Goryushkin, V.F., see Poshevneva, A.I. 182, 208 Goryushkin, V.F., see Tiﬂova, L.A. 216 Goryushkin, V.F., see Tolmach, P.I. 157, 158, 160

Goryushkina, Y.V., see Poshevneva, A.I. 182, 208 Goto, T., see Sekine, C. 15, 25, 26 Goto, T., see Tang, X. 29, 30 Goudiakas, J., see Bettonville, S. 217, 219, 221 Gougoutas, J.Z., see Chang, C.A. 420 Govenloch, L.J., see Clarkson, I.M. 484, 505 Govenlock, L.J., see Bruce, J.I. 355 Gramlich, V., see Hedinger, R. 454 Granado, E. 263, 284, 329 Grande, T., see Faaland, S. 323 Grandjean, F. 8, 13, 23, 24 Grandjean, F., see Long, G.J. 13 Grandjean, F., see Lyon, W.G. 154, 157, 162–164, 166 Grant, D.H. 356 Graves, D.T., see Myers, C.E. 182, 184, 186, 192, 194 Graves, L., see Klink, S.I. 471, 494–496 Greedan, J.E., see Raju, N.P. 43 Greedan, J.E., see Wiebe, C.R. 282 Greenblatt, M., see Markovich, V. 287 Greenblatt, M., see Wiebe, C.R. 282 Greene, R.L., see Chechersky, V. 295, 296, 298, 305, 325 Greene, R.L., see Erwin, R.W. 325 Greene, R.L., see Huang, Q. 289, 325, 328, 329 Greene, R.L., see Nath, A. 325 Greene, R.L., see Smolyaninova, V.N. 321, 327, 329 Greene, R.L., see Zhao, G. 329 Greene, R.L., see Zhao, G.-M. 308 Gregorian, T. 521, 522, 529, 531, 532, 536, 537, 540, 541, 545, 559 Gregorian, T., see Shen, Y.R. 518, 522, 529, 554 Gregorian, T., see Tröster, Th. 521, 522, 531, 533, 536, 541, 545, 546, 551 Greis, O. 149, 150, 166, 200–203, 559 Greis, O., see Petzel, T. 235 Greneche, J.M., see Hannoyer, B. 325 Grenier, J.-C., see Töpfer, J. 286, 287, 289 Grenthe, I. 381, 404, 467, 474, 498–500 Grenthe, I., see Eliet, V. 474, 498, 501 Groen, P.C. 186, 190, 228, 229, 231 Grøonvold, F., see Westrum Jr., E.F. 154 Gross, R., see Klingeler, R. 315 Gross, R., see Reutler, P. 326 Gross, R., see Uhlenbruch, S. 317 Gruber, J.B., see Chang, N.C. 538 Gruber, J.B., see Wells Jr., J.C. 186, 227, 229, 230 Grund, I. 40, 42, 96 Gruzdev, V.P. 499

AUTHOR INDEX Gruzdev, V.P., see Ermolaev, V.L. 495, 497, 499, 501, 503 Grytsiv, A., see Bauer, E. 24 Grzechnik, A., see Loa, I. 268 Gschneidner, K.A., see Adroja, D.T. 60, 61, 118 Gschneidner Jr., K.A. 171, 199 Gschneidner Jr., K.A., see Niu, X.J. 82 Guardigli, M., see Ulrich, G. 358 Güdel, H.U., see Gamelin, D.R. 355 Guertin, R.P., see Meisner, G.P. 6, 12 Guertin, R.P., see Torikachvili, M.S. 6, 8, 17, 22 Guidi, G., see Allodi, G. 325 Guidi, G., see Cestelli Guidi, M. 264 Guilaran, I.J., see Hudspeth, H.D. 326 Guloy, A.M. 49 Gunnlaugsson, T., see Bruce, J.I. 355 Gunnlaugsson, T., see Dickins, R.S. 481 Gunselius, H. 151 Guo, C. 524, 539 Gupta, A., see Xiao, G. 328 Gupta, L.C., see Patil, S. 53, 56, 80, 133 Gupta, R., see Joshi, J.P. 336 Guseinov, G.A., see Kuliev, A.N. 74 Guseinov, G.G., see Aliev, O.M. 77 Guseinov, M.S., see Aliev, O.M. 77 Guseinov, M.S., see Rustamov, P.G. 77 Gutowsky, H.S., see Stout, E.W. 357, 371 Guzik, A. 54, 113 Guzik, A., see Kaczmarska, K. 80 Gvelesiani, G.G. 210, 214 Gvelesiani, G.G., see Yashvili, T.S. 215 Haas, Y. 471, 472, 475–477, 480 Haberkorn, R., see Shen, Y.R. 564 Habermeier, H.U., see Casa, D. 315 Hachisu, D., see Scully, A.D. 489 Haga, Y., see Kohgi, M. 521 Haga, Y., see Naka, T. 521 Haga, Y., see Okayama, Y. 521 Haga, Y., see Oohara, Y. 521 Haga, Y., see Yoshizawa, H. 521 Haines, J., see Bungenstock, C. 540 Haire, R.G. 558 Haire, R.G., see Chen, G. 522–524, 549, 550, 557, 558 Haire, R.G., see Del Cul, G.D. 558 Haire, R.G., see Gibson, J.K. 192, 234 Haire, R.G., see Morrison, H.G. 151, 205 Haire, R.G., see Peterson, J.R. 522, 558 Haire, R.G., see Stump, N.A. 523, 557 Haire, R.G., see Wilmarth, W.R. 521, 522, 558

605

Haire, R.G., see Young, J.P. 558 Halton, M.P., see Golding, R.M. 357, 360, 365, 366, 372 Hamaya, N., see Shirotani, I. 13 Hambley, T.W., see Baker, M.V. 356 Hamilton, J.J., see Smolyaninova, V.N. 321 Hammel, P.C., see Yoshinari, Y. 328 Han, P.D., see Yoon, S. 326 Handy, C., see Spencer, S. 493 Hanﬂand, M., see Loa, I. 268 Hannay, M.H. 236 Hannay, M.H., see Myers, C.E. 237 Hannoyer, B. 325 Hansen, L.D., see Baker, F.B. 214 Harada, M., see Park, Y.Y. 489, 491, 492, 498 Harada, M., see Yamamura, T. 491, 492 Harakas, G., see Forsberg, J.H. 357, 358, 374, 380, 427–431, 439, 440 Hargittai, M. 184, 186, 190, 191, 224, 228–230, 232 Hargittai, M., see Molnár, J. 185, 186, 190, 191, 230–232 Harima, H. 8, 9 Harima, H., see Sugawara, H. 8, 9, 23 Harris, A.L. 204 Harrison, E.R. 236, 238 Harrowﬁeld, J.M. 405–407 Hartinger, C., see Mayr, F. 315 Hartjes, K. 44, 53, 59, 66, 73, 79, 82, 84, 86, 88, 89, 92, 106, 115–117 Haschke, J.M., see Deline, T.A. 161, 163 Haschke, J.M., see Greis, O. 149, 150 Hase, W., see Steinfeld, J. 487 Hasegawa, H., see Anderson, P.W. 258 Hasegawa, Y. 479, 480 Hastie, J.W. 186, 191, 193, 197, 224, 225, 236, 237 Hastie, J.W., see Hauge, R.H. 186, 225, 226 Hatano, M., see Konami, H. 441–443 Hauback, B.C., see Brinks, H.W. 275, 276 Hauge, R.H. 186, 225, 226 Hauge, R.H., see Hastie, J.W. 186, 191, 224, 225 Hauser, W., see Fanghänel, T. 500 Hauser, W., see Kim, J.I. 496 Hautot, D., see Long, G.J. 13 Hawkes, G.E. 368 Hayashi, M., see Nanba, T. 20 Hayes, A.V. 522–524, 571, 572 Hayes, W., see Kusters, R.M. 290 Hazen, R.M. 518 He, J., see Zhu, C. 326 He, Y., see Guo, C. 524, 539

606

AUTHOR INDEX

Hedinger, R. 454 Hedinger, R., see Toth, E. 363, 454 Hedo, M., see Sugawara, H. 8, 9, 23 Heffner, R.H. 298, 325 Heffner, R.H., see Neumeier, J.J. 299 Hegetschweiler, K., see Hedinger, R. 454 Hegetschweiler, K., see Toth, E. 363, 454 Hejtmánek, J., see Jirák, Z. 275 Hejtmánek, J., see Krupicka, S. 330, 338 Heller, A. 475, 476, 480 Hellwege, K.H. 516, 523, 526 Helm, L., see Powell, D.H. 361 Helm, L., see Toth, E. 363, 454 Hemberger, J., see Mayr, F. 315 Hemmilä, I. 509 Henderson, D.C. 162, 164, 203 Henderson, D.C., see Spedding, F.H. 162, 164, 165, 176, 178, 200–203 Hendrawan, H., see Simonin, J.P. 488, 491 Hennig, C. 213–215 Hennig, H., see Billing, R. 489, 491 Hennion, M. 311, 324 Hennion, M., see Biotteau, G. 325 Hennion, M., see Cestelli Guidi, M. 264 Hennion, M., see Moussa, F. 324 Hennion, M., see Rodríguez-Carvajal, J. 263, 275 Henry, B., see Giroux, S. 494, 505 Herbstritt, F., see Reutler, P. 326 Hernando, A., see Alonso, J. 324 Herrero, E., see Fernández-Díaz, M.T. 329 Herrmannsdorfer, T., see Keller, L. 17, 23 Hervieu, M., see Autret, C. 338 Hervieu, M., see Chechersky, V. 298 Hervieu, M., see Damay, F. 330, 336 Hess, C., see Kim, K.H. 327 Hess, N.J. 523, 553, 554 Hickel, B., see Arvis, M. 497 Hiebl, K., see Flandorfer, H. 91, 92, 118, 127 Hiebl, K., see Sologub, O. 41, 43, 45–49, 51–54, 56–63, 66–69, 72–76, 79–84, 86–89, 91, 93, 103, 119–122 Hiebl, K., see Weitzer, F. 44, 59, 65, 73 Higashiyama, N., see Jiang, J. 479, 483, 494 Hill, J.P., see Casa, D. 315 Hill, J.P., see Kiryukin, V. 291 Hill, J.P., see Murakami, Y. 263 Hill, J.P., see Zimmermann, M.V. 264 Hilpert, K. 149, 239 Hilpert, K., see Gietmann, C. 194, 196, 197, 207, 209, 238–240 Hilscher, G., see Bauer, E. 24

Hinckley, C.C. 357 Hino, O., see Yamada, Y. 315 Hinton, J.F. 493 Hirai, T., see Tang, X. 29, 30 Hiraishi, J., see Kanno, H. 482 Hirao, K., see Soga, N. 523, 555 Hirayama, C. 196, 197, 239, 240 Hirayama, F., see Inokuti, M. 577 Hirayama, S., see Scully, A.D. 489 Hirayama, T., see Lee, C.H. 20 Hirota, K., see Endoh, Y. 315 Hirota, K., see Martin, M.C. 322 Hirota, K., see Murakami, Y. 263 Hirota, K., see Nojiri, H. 317 Hnatejko, Z. 482, 496 Ho, P.-C., see Bauer, E.D. 21, 22 Ho, P.-C., see Maple, M.B. 22 Hochheimer, H.D., see Bolduan, F. 522, 550, 566 Hochheimer, H.D., see Urland, W. 521, 545 Hodges, J., see Grandjean, F. 24 Hoeft, S. 421, 422 Hoekstra, H.R. 557 Höfener, C., see Reutler, P. 326 Hofer, J., see Zhao, G.-M. 305, 307 Hoffman, W.K. 45, 48, 53, 56, 59, 61, 67, 69, 73–75, 77, 79, 82, 84, 86, 88, 99, 139 Hofmann, M., see Pissas, M. 329 Hofstraat, J.W., see Klink, S.I. 471, 494–496 Hogg, R.A. 524, 555, 579 Hogg, R.A., see Takarabe, K. 524, 579 Hohmann, E. 210–214, 216, 218, 220, 222 Hohmann, E., see Bommer, H. 174, 210–215, 217–221 Høier, R., see Faaland, S. 323 Holah, D.G., see Brown, D. 152 Holley Jr., C.E., see Baker, F.B. 214 Holley Jr., C.E., see Fitzgibbon, G.C. 210, 212, 215–217 Holley Jr., C.E., see Huber Jr., E.J. 218 Holliday, B.J. 355 Holmes, N.C., see Yoo, C.S. 522, 549, 550 Holokhonova, L.I., see Rezukhina, T.N. 209, 212 Hölsa, J., see Chen, G. 523, 529 Holz, M., see Sacco, A. 482 Holz, R.C. 474, 478, 480, 482, 502 Holz, R.C., see Brink, J.M. 364 Holzapfel, B., see von Helmolt, R. 290 Holzapfel, W.B. 517, 518 Holzapfel, W.B., see Bungenstock, C. 521, 529, 532–535, 537, 540–544, 546

AUTHOR INDEX Holzapfel, W.B., see Gregorian, T. 521, 522, 529, 531, 532, 536, 537, 540, 541, 545, 559 Holzapfel, W.B., see Huber, G. 523, 530 Holzapfel, W.B., see Jayasankar, C.K. 522, 547, 581 Holzapfel, W.B., see Lorenz, B. 522, 554 Holzapfel, W.B., see Noack, R.A. 518 Holzapfel, W.B., see Shen, Y.R. 518, 522, 523, 529, 533, 534, 541, 542, 544–546, 548, 554, 564, 581 Holzapfel, W.B., see Tröster, Th. 521, 522, 531–533, 536, 541–543, 545, 546, 550, 551 Holzer, W. 506 Homes, C.C., see Franck, J.P. 307 Hömmerich, U., see Culp, T.D. 524, 578, 579 Hong, C.S. 326 Honma, T., see Matsuda, T.D. 17 Hope, H., see Chan, J.Y. 37 Hope, H., see Stetson, N.T. 15 Hopfgartner, G., see Bocquet, B. 453, 455, 456 Hopfgartner, G., see Floquet, S. 453, 455–459 Hopfgartner, G., see Petoud, S. 355, 384–387 Hopfgartner, G., see Piguet, C. 355, 393–395 Hopfgartner, G., see Renaud, F. 387–393, 408 Hopfgartner, G., see Rigault, S. 358, 361, 363, 366, 378, 396–400 Hopkins, T.A. 369, 377, 381, 383, 400, 405, 410 Hopkins, T.A., see Dewey, H.J. 467 Hori, M., see Shirotani, I. 13 Horikoshi, Y., see Taguchi, A. 525, 578 Hornbostel, M.D. 8 Horrocks Jr., W.deW. 357, 367, 368, 372, 379, 477–480, 484, 495, 497, 499, 501, 503, 504, 507 Horrocks Jr., W.deW., see Albin, M. 478, 499, 505 Horrocks Jr., W.deW., see Breen, P.J. 473, 474 Horrocks Jr., W.deW., see Frey, S.T. 496 Horrocks Jr., W.deW., see Holz, R.C. 474, 478, 480, 482, 502 Horrocks Jr., W.deW., see Supkowski, R.M. 481–483 Horrocks Jr., W.deW., see Wang, Y. 478, 494 Horrocks Jr., W.deW., see Wong, C.P. 449 Horrocks Jr., W.deW., see Wu, S. 469, 499 Horrocks Jr., W.deW., see Wu, S.L. 492 Hossain, Z., see Patil, S. 53, 80, 133 Houshiar, M., see Thornton, M.J. 124 Howard, J.A.K., see Aime, S. 426, 429 Howard, J.A.K., see Parker, D. 420 Hu, J., see Dagotto, E. 261 Hu, S., see Meisner, G.P. 11 Hu, S., see Morelli, D.T. 11

607

Hu, Y.F., see Ren, Y.H. 326 Hu, Z. 521 Hua, H. 521, 522, 552, 553 Huan, C.H.A., see Li, J.-M. 325 Huang, Q. 289, 325, 328, 329 Huang, Q., see Lynn, J.W. 299, 325 Hubbard, J. 260 Hubbard, W.N., see Fuger, J. 171 Hubbard, W.N., see Johnson, G.K. 209, 210, 212, 213, 215–217, 219, 220 Hubbard, W.N., see Lyon, W.G. 154, 157, 162–164, 166 Huber, G. 523, 530 Huber Jr., E.J. 218 Huber Jr., E.J., see Fitzgibbon, G.C. 212, 215 Hubert, S., see Billard, I. 470, 495, 501–503, 506 Hubert, S., see Thouvenot, P. 507 Hubert, T.D., see Montgomery, R.L. 214 Hücker, M., see Uhlenbruch, S. 317 Hudspeth, H.D. 326 Hueso, L.E. 326 Hueso, L.E., see Mira, J. 295, 310 Hueso, L.E., see Rivadulla, F. 309, 321 Huhtinen, H. 326 Hulliger, F. 48, 49, 78, 94, 140 Hulliger, F., see Frick, B. 94, 140 Hulliger, F., see Ott, H.R. 55 Hundley, M.F., see Neumeier, J.J. 299 Hunt, M.B., see Zhao, G.-M. 305, 307 Huntelaar, M.E., see Cordfunke, E.H.P. 152, 207, 208 Hur, N.H., see Dho, J. 322 Hur, N.H., see Hong, C.S. 326 Hurtgen, C. 210, 212–214, 216, 218, 220 Hushagen, R.W., see Bollore, G. 43, 47, 49, 50, 55, 57, 58, 60, 62, 69, 71, 72, 74, 75, 110 Hushagen, R.W., see Ferguson, M.J. 43, 47, 49, 50, 58, 62, 63, 72, 79, 82, 84 Hushagen, W., see Ferguson, M.J. 49, 57, 61, 70, 75, 103 Huskens, J., see Peters, J.A. 356–359, 362, 368, 373, 380 Huskens, J., see Sherry, A.D. 433 Huskowska, E. 405 Husson, C., see Chapon, D. 454, 455 Hutchinson, F. 179 Hwang, H.Y. 290, 291 Hwang, H.Y., see Chen, C.H. 329 Hwang, H.Y., see Fernández-Baca, J.A. 321 Hwang, H.Y., see Radaelli, P.G. 299, 323, 325 Hyer, E.J., see Hornbostel, M.D. 8

608

AUTHOR INDEX

Iannone, G., see Radaelli, P.G. 299, 323 Ibañez, G., see Causa, M.T. 326 Ibarra, M.R., see De Teresa, J.M. 298–300 Ibarra, M.R., see García-Landa, B. 338 Ideka, S., see Moriyasu, M. 504 Igarashi, K. 203–205 Ikebe, M., see Fujishiro, H. 276, 322, 326 Ikeda, S., see Kohgi, M. 521 Ikeda, S., see Moriyasu, M. 489, 491 Ikeda, S., see Yokoyama, Y. 491, 497 Ikezawa, M., see Kimura, S. 130 Il’ina, L.D., see Khanaev, E.I. 209, 213, 214 Ilisavskii, Y. 326 Imbert, D., see Floquet, S. 453, 455–459 Inaba, T., see Sekine, C. 20, 24 Inada, Y., see Sugawara, H. 18 Inagawa, I., see Sekine, C. 13 Inami, T., see Yamada, Y. 315 Inokuti, M. 577 Inoue, J., see Ishihara, E. 269 Inoue, M., see Sekine, C. 24 Ioannidis, N., see Papavassiliou, G. 328 Ioannou, A.G., see Spencer, S. 493 Ippolitov, E.G., see Gogadze, N.G. 201–203 Ippolitov, E.G., see Rezukhina, T.N. 209, 212 Ippolitov, E.G., see Zhigarnovskii, B.M. 201, 203 Ireland, J.R., see Kim, S.-J. 92 Irwin, J.C., see Franck, J.P. 307 Isaac, I., see Chechersky, V. 295, 296, 305, 325 Isaac, I., see Franck, J.P. 307 Isaac, I., see Gordon, J.E. 326 Isaacs, N.S., see Holzapfel, W.B. 517 Ishibashi, T., see Tanaka, F. 484, 491, 492 Ishigame, M., see Arashi, H. 524, 529, 553, 554 Ishigure, K., see Katsumura, Y. 489, 496, 497, 508 Ishigure, K., see Nagaishi, R. 497 Ishihara, E. 269 Ishihara, S., see Endoh, Y. 315 Ishihara, S., see Saitoh, E. 269 Ishii, M., see Lee, C.H. 20 Ishii, T., see Park, Y.Y. 489, 491, 492, 498 Ishikawa, M. 41, 101 Ishikawa, M., see Kanai, K. 13 Ishikawa, M., see Takeda, N. 8, 12, 15–17, 21, 23, 24 Ishiwata, E., see Hasegawa, Y. 479, 480 Itoh, M., see Mahesh, R. 329 Ivchenko, L.A., see Voloshin, V.A. 521, 559 Iwadate, Y. 179 Iwai, A., see Kumagai, K. 311 Iwamaru, S.I., see Yayamura, T. 473

Iwata, S., see Yayamura, T. 473 Izotov, A.I., see Krygin, I.M. 522 Jaccarino, V., see Shrivastava, K.N. 279, 280 Jackson, J.A., see Lewis, W.B. 364 Jacques, V. 423 Jaime, M. 300 Jaime, M., see Sakaie, K.E. 296 Jaksic, Z.M., see Urosevic, V.V. 522 Jamieson, J.C. 516 Janik, M.B.L., see Allegrozzi, M. 363 Janik, M.B.L., see Bertini, I. 374 Janossy, A., see Dupont, F. 336 Janossy, A., see Toth, E. 363, 454 Janssens, L.D. 471 Jantsch, W. 525, 580 Jantsch, W., see Przybylinska, H. 525, 580 Jardón, C., see Rivadulla, F. 309 Jasien, P.G., see Stevens, W.J. 148 Jayaraman, A. 519 Jayasankar, C.K. 522, 547, 581 Jayasankar, C.K., see Lavin, V. 522 Jefferson, D.A., see Reller, A. 282 Jeitschko, W. 2, 4, 6, 7, 15, 23, 24 Jeitschko, W., see Albering, J.H. 76, 90 Jeitschko, W., see Altmeyer, R.O. 37 Jeitschko, W., see Braun, D.J. 2, 4, 7, 11, 15, 44, 47, 49, 52, 56, 57, 59, 60, 62, 69, 71, 76–78 Jeitschko, W., see Brylak, M. 42, 43, 48, 50, 56, 58, 61, 62, 69, 72, 75, 81, 83, 85, 87, 89, 90 Jeitschko, W., see Dannebrock, M.E. 10, 21, 23, 24 Jeitschko, W., see Evers, C.B.H. 15, 23 Jeitschko, W., see Evers, Ch.B.H. 65, 71, 72, 74, 76, 77, 95 Jeitschko, W., see Grandjean, F. 8, 13, 23, 24 Jeitschko, W., see Hartjes, K. 44, 53, 59, 66, 73, 79, 82, 84, 86, 88, 89, 92, 106, 115–117 Jeitschko, W., see Hoffman, W.K. 45, 48, 53, 56, 59, 61, 67, 69, 73–75, 77, 79, 82, 84, 86, 88, 99, 139 Jeitschko, W., see Kaiser, J.W. 4, 15, 52 Jeitschko, W., see Marchand, R. 76, 79 Jeitschko, W., see Rühl, R. 76, 90 Jeitschko, W., see Schmidt, T. 94, 135, 140 Jeitschko, W., see Wollesen, P. 43, 44, 46, 48, 49, 51, 52, 54, 57–61, 63, 66, 68, 70, 72, 73, 75, 80, 83 Jenkins, A.L. 507 Jezierski, A., see Slebarski, A. 45, 59, 60, 100, 113 Jia, Y.Q. 184 Jiang, J. 479, 483, 494

AUTHOR INDEX Jin, R., see Sales, B.C. 11 Jirák, Z. 275, 291 Jirák, Z., see Damay, F. 330 Jirák, Z., see Krupicka, S. 330, 338 Johannsen, P.G. 561, 564 Johannsen, P.G., see Tröster, Th. 522, 536 Johansson, B. 199 Johnson, C.E., see Kim, K.-Y. 170, 171 Johnson, D.C., see Hornbostel, M.D. 8 Johnson, G.K. 209, 210, 212, 213, 215–217, 219, 220 Johnson, G.K., see Lyon, W.G. 154, 157, 162–164, 166 Jones, D.A. 200–203 Jonker, G.H. 265 Jorda, J.L., see Ishikawa, M. 41, 101 Jørgensen, C.K. 497, 529, 541 Jorgensen, J.D., see Chmaissem, O. 278, 280 Jorgensen, J.D., see Dabrowski, B. 311 Jorgensen, J.D., see Radaelli, P.G. 299, 323 Jorgensen, J.D., see Xiong, X. 311 Joshi, J.P. 336 Joubert, L. 182, 183, 187–189 Jovani´c, B.R. 522, 524, 563 Jovani´c, B.R., see Urosevic, V.V. 522 Ju, H., see Chechersky, V. 295, 296, 325 Judd, B.R. 400, 547, 560 Jukes, R.T.F., see Werts, M.H.V. 481 Jun-Hao, X., see Chen, B. 13 Jung, G., see Yuzhelevski, Y. 326 Jung, J.H. 323 Jung, J.H., see Dho, J. 325 Jung, J.H., see Kim, K.H. 296 Junod, A., see Ishikawa, M. 41, 101 Juretschke, P., see Paulus, E.F. 430, 433 Kachmarska, K., see Skolozdra, R.V. 52, 112, 113, 117, 120–123 Kacprzak, L., see Massalski, T.B. 36 Kaczmarska, K. 80, 112, 113 Kaczmarska, K., see Guzik, A. 54 Kaczorowski, D., see Leithe-Jasper, A. 26 Kaeser, M., see Nolas, G.S. 29, 30 Kafalas, J.A., see Goodenough, J.B. 250, 251, 277, 282 Kahn, O. 355, 360, 366, 368 Kaindl, G., see Hu, Z. 521 Kaiser, J.W. 4, 15, 52 Kajimoto, R. 337 Kajimoto, R., see Kawano, H. 311, 336 Käll, M., see Björnsson, P. 268

609

Kallias, G. 328 Kallias, G., see Papavassiliou, G. 325, 328 Kallias, G., see Pissas, M. 329 Kallias, G., see Simopoulos, A. 328 Kaltsoyannis, N. 366 Kamada, M., see Kimura, S. 130 Kamenev, K., see Allodi, G. 328, 337 Kamenev, K., see De Teresa, J.M. 300 Kamenev, K.V., see Zvyagin, S. 338 Kamenev, V.I., see Zvyagin, S. 338 Kaminski, R. 507 Kana’an, A., see Kent, R.A. 234 Kanai, K. 13 Kanamori, J. 263 Kanao, R., see Yamada, Y. 315 Kanatsidis, M.G., see Kim, S.-J. 92 Kanazawa, M., see Kim, Y.C. 217, 220 Kaneko, K., see Endoh, Y. 315 Kaneko, K., see Nojiri, H. 317 Kang, D.J., see Zhao, G.-M. 308 Kang, D.W., see Lee, K.P. 492 Kang, S.H., see Kim, Y.C. 214, 215, 221 Kankare, J., see Latva, M. 494, 495 Kannewurf, C.R., see Kim, S.-J. 92 Kanno, H. 482 Kanoda, K., see Shirotani, I. 7, 9, 21 Kanoda, K., see Uchiumi, T. 7–9, 12 Kao, C.-C., see Zimmermann, M.V. 264 Kapala, J. 190, 191, 193, 232, 233, 236, 237 Kaposi, O. 196, 240 Kappelmann, H.-G., see Buchler, J.W. 449 Karabashev, S.G., see Quijada, M.A. 269 Karabashev, S.G., see Smolyaninova, V.N. 321 Karagodina, A.M., see Molodkin, A.K. 208 Kasai, M., see Chahara, K.I. 290 Kasai, M., see Kuwahara, H. 333 Kasatochkin, S.V. 524 Kasaya, M. 49, 57, 58, 62, 129–132 Kasaya, M., see Katoh, K. 130, 132 Kasaya, M., see Kimura, S. 130 Kasaya, M., see Suzuki, H. 58, 78 Kasper, N.V., see Troyanchuk, O.Ya. 275 Kasuga, K. 440 Kasyanov, A.I., see Voloshin, V.A. 523, 524 Kataky, R., see Blair, S. 509 Katano, S., see Yamada, Y. 315 Kataoka, M. 263 Kato, Y., see Fanghänel, T. 500 Kato, Y., see Kimura, T. 471–474, 478, 479, 481 Kato, Y., see Nagaishi, R. 497 Kato, Y., see Takahashi, K. 481

610

AUTHOR INDEX

Katoh, K. 118, 130, 132 Katoh, K., see Kasaya, M. 49, 57, 58, 62, 129–132 Katoh, K., see Kimura, S. 130 Katoh, T., see Suzuki, H. 58, 78 Katsufuji, T. 275 Katsufuji, T., see Machida, A. 336 Katsumura, Y. 489, 496, 497, 508 Katsumura, Y., see Nagaishi, R. 497 Katz, J.J. 467, 500 Kaul, A., see Shames, A.I. 338 Kaul, A., see Yakubovskii, A. 309 Kaul, A.R., see Babushkina, N.A. 308, 309, 327 Kauzlarich, S.M., see Chan, J.Y. 37, 90, 134 Kauzlarich, S.M., see Fisher, I.R. 90, 91, 134, 135, 137 Kauzlarich, S.M., see Rehr, A. 76, 111 Kauzlarich, S.M., see Stetson, N.T. 15 Kauzlarich, S.M., see Xue, J.S. 12 Kawai, T., see Liu, X.J. 299 Kawakami, T., see Shirotani, I. 9, 10 Kawano, H. 311, 336 Kawano, H., see Kajimoto, R. 337 Kawano, H., see Yoshizawa, H. 291 Kawasaki, Y., see Tanaka, F. 471, 472 Kawata, H., see Murakami, Y. 263 Kazakov, V.P., see Khamidullina, L.A. 497 Keating, K.B. 521–525, 562 Keen, D.A., see Kusters, R.M. 290 Keenan, T.K., see Carnall, W.T. 494 Keimer, B., see Casa, D. 315 Keimer, B., see Kiryukin, V. 291 Keller, H., see Alexandrov, A.S. 308 Keller, H., see Zhao, G. 326, 329 Keller, H., see Zhao, G.-M. 305, 307, 308 Keller, L. 17, 23 Keller, N., see Arvis, M. 497 Kemp, T.J., see Allsopp, S.R. 473, 474 Kemp, T.J., see Baird, C.P. 497, 498 Kemple, M.D. 357, 358, 367, 373–375, 386 Kennedy, R.J. 521, 522, 524, 525 Kent, R.A. 234 Keppens, V. 11 Keppens, V., see Chakoumakos, B.C. 8 Keppens, V., see Sales, B.C. 7, 9–11, 13, 29, 31 Kessler, M.A. 486, 508 Khairulin, R.A. 178, 202 Khairulin, R.A., see Stankus, S.V. 150, 200–203 Khamidullina, L.A. 497 Khanaev, E.I. 209, 213, 214 Khanaev, E.I., see Storozhenko, T.P. 215–217 Khasaev, J.P., see Rustamov, P.G. 74, 77

Khasanshin, I.V., see Kudin, L.S. 193, 237 Kholokhova, L.I. 211, 213, 215, 216, 221 Khomskii, D.I., see Babushkina, N.A. 308, 309, 327 Khomskii, D.I., see Mizokawa, T. 263 Khudiakov, I.V., see Azenha, M.E. 498 Khudyakov, I., see Rykov, S. 497 Kido, G., see Urushibara, A. 311 Kiefer, G.E., see Geraldes, C.F.G.C. 430, 433, 435, 439, 440 Kierspel, H., see Uhlenbruch, S. 317 Kihn-Botulinski, M., see Buchler, J.W. 449–452 Kijowski, J., see Burgess, J. 221 Kikuchi, C., see Morrison, C. 530 Kikuchi, T., see Fujishiro, H. 326 Kim, I., see Dho, J. 325, 328 Kim, J.I. 496 Kim, J.I., see Aas, W. 500 Kim, J.I., see Billard, I. 470, 495, 501–503, 506 Kim, J.I., see Fanghänel, T. 495, 496, 500 Kim, J.I., see Klenze, R. 500 Kim, J.I., see Monsallier, J.M. 506 Kim, J.I., see Morgenstern, M. 506 Kim, J.I., see Panak, P. 494, 495 Kim, J.I., see Paviet, P. 500 Kim, J.I., see Wimmer, H. 500 Kim, K.-Y. 170, 171 Kim, K.H. 296, 327, 328 Kim, K.H., see Dho, J. 325 Kim, K.H., see Jung, J.H. 323 Kim, K.H., see Naler, S. 328 Kim, K.Y., see Johnson, G.K. 209, 210, 212, 213, 215–217, 219, 220 Kim, S.-J. 92 Kim, T.H., see Uehara, M. 323 Kim, W.S., see Dho, J. 322 Kim, W.S., see Hong, C.S. 326 Kim, Y., see Harrowﬁeld, J.M. 405–407 Kim, Y.-J., see Zimmermann, M.V. 264 Kim, Y.C. 213–215, 217, 219–221 Kimball, C.W., see Dabrowski, B. 311 Kimball, C.W., see Xiong, X. 311 Kimura, H., see Endoh, Y. 315 Kimura, S. 130 Kimura, S., see Shirotani, I. 13 Kimura, T. 336, 471–474, 478, 479, 481 Kimura, T., see Arisaka, M. 473, 474, 481 Kimura, T., see Billard, I. 470, 495, 501–503, 506 Kimura, T., see Lis, S. 489, 491 Kimura, T., see Nagaishi, R. 497 Kimura, T., see Saitoh, E. 269

AUTHOR INDEX Kimura, T., see Takahashi, K. 481 Kimura, T., see Tobe, K. 266, 269 King, E.G. 154, 164, 176, 178, 200 Kinoshita, M., see Shirotani, I. 7–9, 12 Kirsch, B., see Berthoud, T. 507, 508 Kiryukin, V. 291 Kiseleva, T.V. 204 Kiseleva, T.V., see Laptev, D.M. 203, 204, 210–212, 216 Kishenbaum, A.D. 178 Kjekshus, A., see Brinks, H.W. 275, 276 Klakamp, S.L., see Holz, R.C. 502 Klamut, P.W., see Dabrowski, B. 311, 323 Klein, G., see Bouby, M. 474 Klein, M.P., see Vold, R.L. 364 Kleinke, H. 37 Klenze, R. 495, 500 Klenze, R., see Billard, I. 470, 495, 501–503, 506 Klenze, R., see Fanghänel, T. 500 Klenze, R., see Kim, J.I. 496 Klenze, R., see Morgenstern, M. 506 Klenze, R., see Panak, P. 494, 495 Klenze, R., see Paviet, P. 500 Klenze, R., see Wimmer, H. 500 Klimov, A., see Ilisavskii, Y. 326 Klingeler, R. 315 Klingeler, R., see Uhlenbruch, S. 317 Klink, S.I. 471, 494–496 Kloc, C., see Fernández-Baca, J.A. 321 Klose, H., see Vogel, R. 36 Klüfers, P. 77, 91 Knoff, M., see Buchler, J.W. 449 Knudsen, K.D., see Faaland, S. 323 Kobayashi, S., see Shimomura, S. 326, 327 Kobzenko, G.F. 36 Koehler, W.C. 259 Koehler, W.C., see Wollan, E.O. 262, 327 Kohgi, M. 521 Kohgi, M., see Kasaya, M. 131, 132 Kohgi, M., see Okayama, Y. 521 Kohgi, M., see Oohara, Y. 521 Kohgi, M., see Yoshizawa, H. 521 Kojima, T., see Park, Y.Y. 489, 491, 492, 498 Kok-Scheele, A., see Konings, R.J.M. 208 Kolenda, M., see André, G. 123 Kolesnik, S., see Chmaissem, O. 278, 280 Kolesnik, S., see Xiong, X. 311 Kolonits, M., see Molnár, J. 185, 186, 190, 191, 230–232 Komarov, S.A., see Ezhov, Y.S. 230 Konami, H. 441–443

611

Konings, R.J.M. 156, 208 Konings, R.J.M., see Cordfunke, E.H.P. 171, 172, 174, 220, 221 Konings, R.J.M., see Kovács, A. 183–186, 189, 190, 227–230 Konings, R.J.M., see Molnár, J. 185, 186, 190, 191, 230–232 Konnecke, T., see Fanghänel, T. 500 Konno, Y., see Fujishiro, H. 322 Koo, T.Y., see Podzorov, V. 327 Korshunov, B.G. 204, 205 Korshunov, B.G., see Pashinkin, A.S. 237 Kotliar, G., see Rozenberg, M.J. 261, 315 Kotov, M.G., see Khanaev, E.I. 209, 213 Kotzyba, G., see Jeitschko, W. 15, 23, 24 Kourouklis, G.A., see Urland, W. 521, 545 Kovács, A. 183–186, 189–191, 198, 227–230, 232, 233 Kovacs, Z., see Zhang, S. 355 Koyama, I., see Murakami, Y. 263 Koyama, Y., see Iwadate, Y. 179 Kozanecki, A., see Stapor, A. 525, 578 Kozono, Y., see Chahara, K.I. 290 Kozyrkov, V.V., see Aliev, F.G. 118 Krasnov, A.V., see Girichev, G.V. 229 Krasnov, A.V., see Giricheva, N.I. 184, 190, 191, 193, 228, 232 Krasnov, K.S. 227 Krasnov, K.S., see Giricheva, N.I. 229 Krasnova, O.G., see Girichev, G.V. 229 Krasnova, O.G., see Giricheva, N.I. 184, 190, 191, 193, 228, 232 Krauss, M., see Stevens, W.J. 148 Krayevski, J.J., see Cava, R.J. 56 Kremer, R., see Urland, W. 521, 545 Krieger, Y.G., see Babailov, S.P. 357 Krimnus, M.G., see Voloshin, V.A. 521 Krohina, A.G., see Molodkin, A.K. 208 Krok-Kowalski, J., see Büchel, D. 151, 206 Kronenberg, A., see Billard, I. 470, 495, 501–503, 506 Kropp, J.L. 475–477, 480 Kruk, R., see Chmaissem, O. 278, 280 Krupicka, S. 330, 338 Krupicka, S., see Jirák, Z. 291 Krupski, M., see Rewaj, T. 523, 524, 536 Krygin, I.M. 521, 522, 536 Krystkowiak, E., see Sikorski, M. 489 Krzhizhanovskaya, see Suvorov, A.V. 234 Kubo, H., see Iwadate, Y. 179 Kubota, M., see Kawano, H. 311

612

AUTHOR INDEX

Kudin, L.S. 193, 237, 238 Kudin, L.S., see Pogrebnoi, A.M. 193, 194, 236, 237 Kuech, T.F., see Culp, T.D. 524, 525, 578–580 Kugel, K.I., see Babushkina, N.A. 308, 309, 327 Kulagin, N.A., see Voloshin, V.A. 522, 531 Kulagin, N.M., see Laptev, D.M. 203, 204 Kuliev, A.N. 74 Kumagai, K. 311 Kumagai, K., see Yakubovskii, A. 309 Kumai, R., see Asamitsu, A. 319 Kumai, R., see Kimura, T. 336 Kumai, R., see Kuwahara, H. 333 Kumar, A., see Congeduti, A. 325 Kumar, A., see Meneghini, C. 325 Kumar, D. 326 Kumar, K., see Chang, C.A. 420 Kumbe, M.U., see Monsallier, J.M. 506 Kumke, M., see Billard, I. 470, 495, 501–503, 506 Kunnen, B., see Jeitschko, W. 15, 23, 24 Kupchikov, A.K. 525, 581, 582 Kuriata, J., see Rewaj, T. 524, 536 Kurita, A., see Nishimura, G. 524 Kushida, T., see Mishimura, G. 557 Kushida, T., see Nishimura, G. 524 Kusters, R.M. 290 Kusukawa, T., see Fujita, M. 355 Kutnetsov, A.Y., see Kudin, L.S. 193, 237, 238 Kutscher, J. 208, 209 Kutsenko, A.B., see Dierolf, V. 525, 555 Kuwahara, H. 330, 331, 333, 336, 337 Kuwahara, H., see Asamitsu, A. 291 Kuwahara, H., see Kajimoto, R. 337 Kuwahara, H., see Kawano, H. 336 Kuwahara, H., see Kumagai, K. 311 Kuwahara, H., see Moritomo, Y. 291 Kuwahara, H., see Shimomura, S. 326, 327 Kuwahara, H., see Tokura, Y. 330, 341 Kuwahara, H., see Tomioka, Y. 291 Kuz’ma, Yu.B., see Mozharivskyj, Yu. 41, 82, 84, 86–88, 92, 111, 138, 139 Kuznetsov, V.L. 24, 26 Kvardakov, A.M., see Slovyanskikh, V.K. 94, 95, 140 Kwon, Y.U., see Ganguli, A.K. 42, 110 Kycia, S., see Billinge, S.J.L. 304 Labeau, M. 203 Labet, A., see Billard, I. 510 Lacam, A. 522, 529, 554 Lacam, A., see Leger, J.M. 522, 554 Lacerda, A.H., see Gajewski, D.A. 13

Laenen, R. 482 Lafont, U., see Ravot, D. 10, 11, 13 Lagarde, G., see Billard, I. 470, 495, 501–503, 506 Lagendijk, A., see Schuurmans, F.J.P. 471, 485 Lähderanta, E., see Huhtinen, H. 326 Laiho, R., see Huhtinen, H. 326 Lake, C.H., see Amin, S. 426 Lake, C.H., see Morrow, J.R. 426 Lam, R. 47, 55, 60, 68, 74, 78, 80, 83, 84, 103 Lam, R., see Deakin, L. 133 LaMar, G.N., see Burns, P.D. 363 Lamarque, G., see Billard, I. 470, 495, 501–503, 506 Lang, A., see Jeitschko, W. 15, 23, 24 Lang, J., see Paulus, E.F. 430, 433 Langlois, M.H., see Dubost, J.P. 420 Lanza, G. 189 Lanza, G., see Di Bella, S. 185 Lanza, H., see Levy, P. 328 Lanzara, A. 295, 325 Lanzerstorfer, S., see Jantsch, W. 525, 580 Lanzerstorfer, S., see Przybylinska, H. 525, 580 Lao, K. 506 Laptev, D.M. 203, 204, 210–212, 216 Laptev, D.M., see Kiseleva, T.V. 204 Laszak, I., see Moulin, C. 501 Latva, M. 494, 495 Lauffer, R.B., see Caravan, P. 357, 360–362 Laukhin, V. 299 Laukhin, V., see Fontcuberta, J. 299 Laukhin, V., see Martínez, B. 317 Laukhin, V., see Senis, R. 317 Lavin, V. 522, 523 Lavin, V., see Tröster, Th. 551 Lawrie, D.D., see Franck, J.P. 307 Laws, W.R. 498, 505 Lawson, A.W., see Jamieson, J.C. 516 Lay, K.-L., see Buchler, J.W. 449 Leavitt, R.P., see Chang, N.C. 538 Leavitt, R.P., see Morrison, C.A. 154, 160–162, 167, 371 Lebedev, V.A. 36 Lebedev, Y.S., see Powell, D.H. 361 Lebrun, C., see Bretonnière, Y. 393 Lebrun, C., see Chapon, D. 454, 455 Lee, C.H. 20 Lee, C.H., see Zhao, Y.G. 296 Lee, Ch.-H., see Sekine, C. 13 Lee, D.W., see Chang, C.A. 420 Lee, H.J., see Dho, J. 325 Lee, K.P. 492

AUTHOR INDEX Lee, S., see Dho, J. 325, 328 Lee, S., see Kim, K.H. 328 Lee, Y.-M., see Allegrozzi, M. 363 Lee, Y.-M., see Bertini, I. 374 Lees, M.R. 291 Lees, M.R., see Campbell, A.J. 319 Lees, M.R., see García-Landa, B. 338 Legendre, J.-J., see Joubert, L. 182, 183, 187–189 Leger, J.M. 522, 554 Léger, J.M., see Bungenstock, C. 540 Leger, J.M., see Dubost, J.P. 420 Leger, J.M., see Syassen, K. 525 Lehn, J.-M. 355 Leibfritz, D., see Hawkes, G.E. 368 Leininger, S. 355 Leithe-Jasper, A. 26, 43, 44, 51, 52, 59, 63–66, 72, 73, 79, 96, 100, 104, 138 Leithe-Jasper, A., see Flandorfer, H. 127 Leithe-Jasper, A., see Sologub, O. 42, 48, 56, 61, 69, 75, 81, 83, 85, 87, 88, 90, 92, 93, 102, 119, 120, 123 Leithe-Jasper, A., see Weitzer, F. 44, 59, 65, 73 Lelik, L., see Kaposi, O. 196, 240 Lemons, J.F., see Lewis, W.B. 364 Lena, A., see Tolentino, H. 518 Lenkinski, R.E., see Wilcott, M.R. 373, 385 Leonidov, V.Y. 218 Leonidov, V.Y., see Furkaliouk, M.Y. 217, 220, 221 Leonov, A.V., see Morozkin, A.V. 85 Leonowicz, M.E., see Poeppelmeier, K.R. 282 Lesiecki, M. 186, 224 Le´snievska, B., see André, G. 123 LeToullec, R., see Datchi, F. 522, 554 Levine, B.A., see Bleaney, B. 357, 365, 371 Levy, D., see Meneghini, C. 325 Levy, P. 328 Levy, P., see Freitas, R.S. 328, 329 Lewandowski, S.J., see Ilisavskii, Y. 326 Lewis, E.A., see Baker, F.B. 214 Lewis, G.N. 182 Lewis, M., see Wells Jr., J.C. 186, 227, 229, 230 Lewis, W.B. 364 Leyva, G., see Levy, P. 328 Lezhava, S.A. 219, 220 Li, B., see Guo, C. 524, 539 Li, C.L. 547 Li, H., see Chi, Y. 523, 533, 539 Li, J.-M. 325 Li, J.J., see Zhao, Y.G. 296 Li, J.Q. 329

613

Li, X.G., see Zheng, R.K. 328 Li, Z.Y., see Lynn, J.W. 299, 325 Licci, F., see Allodi, G. 328 Lim, M. 234 Lin, J.G., see Chang, C.W. 336 Lin, J.H., see Zhang, J.S. 65, 73 Lin, P., see Sakaie, K.E. 296 Lincoln, R.L., see Nafziger, R.H. 200 Lindahl, C.B., see Corbett, J.D. 208 Liotta, F.J., see Horrocks Jr., W.deW. 499, 501 Liou, S.H., see McIlroy, D.N. 295 Lipkowitz, K.B., see Kemple, M.D. 357, 358, 367, 373–375, 386 Lippincott, E.R., see Weir, C.E. 516 Lis, S. 471, 473, 478–481, 489, 491, 494, 496 Lis, S., see Billard, I. 470, 495, 501–503, 506 Lis, S., see Hnatejko, Z. 482, 496 Lis, S., see Meinrath, G. 495, 497, 501 Lisowski, J. 357, 358, 364, 374–376 Littleton IV, R.T., see Nolas, G.S. 29, 30 Littlewood, P.B., see Millis, A.J. 268 Liu, G., see Allegrozzi, M. 363 Liu, G.-L. 311, 313, 316, 318 Liu, G.L., see Zhou, J.-S. 311, 316 Liu, H.L. 328 Liu, H.L., see Yoon, S. 326 Liu, J. 523, 553 Liu, S. 523, 524, 529, 530, 533, 539 Liu, S., see Chi, Y. 523, 524, 530, 533, 534, 536, 539 Liu, S., see Wang, L. 523, 524, 551, 568 Liu, X.J. 299 Llobet, A. 336 Llobet, A., see Frontera, C. 336 Loa, I. 268 Lobad, A.I. 326 Lochhead, M.J. 471, 524, 555, 556, 581 Lodeiro, C., see Bazzicalupi, C. 492, 509 Loeb, A.L., see Goodenough, J.B. 262 Löfﬂer, J., see Buchler, J.W. 450–453 Loﬂand, S., see Smolyaninova, V.N. 327 Lohr, H.R. 210, 212 Lohr, L., see Sharp, R. 359 Loidl, A., see Mayr, F. 315 Loktyushina, N.S. 186, 228–231 Löliger, J. 356 Loncin, M.-F., see Spirlet, M.-R. 420 Long, G.J. 13 Long, G.J., see Grandjean, F. 13 Longo, J.M., see Goodenough, J.B. 250, 251, 277, 282

614

AUTHOR INDEX

Longo, J.M., see Poeppelmeier, K.R. 282 Lopez, M. 489, 491, 500, 508 López Quintela, M.A., see Mira, J. 295, 310 López-Quintela, M.A., see Causa, M.T. 326 López-Quintela, M.A., see Hueso, L.E. 326 López-Quintela, M.A., see Rivadulla, F. 305, 309, 321 Lopinski, S., see Bruce, J.I. 355 Lorenz, B. 522, 554 Lorenz, B., see Alexandrov, A.S. 308 Lortz, R., see Gordon, J.E. 326 Losi, P., see Bianchi, A. 426 Lotgering, F.K. 267 Lotnik, S.V., see Khamidullina, L.A. 497 Loubeyre, P., see Datchi, F. 522, 554 Louca, D. 263, 304 Louca, D., see Egami, T. 263, 292 Lövgren, T., see Soini, E. 509 Lowe, M.P., see Blair, S. 509 Lowe, M.P., see Bruce, J.I. 355 Lowe, M.P., see Clarkson, I.M. 484, 505 Lu, L., see Zhao, Y.G. 328 Lu, Q. 298 Lübbers, R. 518 Lucci, F., see Allodi, G. 325 Luchinat, C., see Allegrozzi, M. 363 Luchinat, C., see Bertini, I. 356, 357, 359, 361–364, 366–368, 374 Luchinat, C., see Clementi, V. 359 Lueken, H., see Sologub, O.L. 58, 72, 106 Luke, G.M., see Heffner, R.H. 325 Lukin, S.N. 524, 536 Lun, L., see Wang, Q. 524, 530, 538 Lüpke, G., see Ren, Y.H. 326 Lüthi, B., see Zvyagin, S. 338 Lützenkirchen, K., see Billard, I. 485, 510 Lützenkirchen, K., see Nehlig, A. 473, 474, 482, 485 Lützenkirchen, K., see Rustenholtz, A. 474 Lützenkirchen, K., see Simonin, J.P. 491 Lyapunov, K.M. 164, 165, 176 Lyapunov, K.M., see Khairulin, R.A. 178 Lyapunov, K.M., see Stankus, S.V. 150, 200–203 Lynch, V., see Lisowski, J. 357, 358, 374–376 Lynchak, K.A., see Kobzenko, G.F. 36 Lynn, J.W. 299, 325 Lynn, J.W., see Adams, C.P. 298 Lynn, J.W., see Erwin, R.W. 325 Lynn, J.W., see Huang, Q. 289, 325, 328, 329 Lynn, J.W., see Maple, M.B. 22 Lynn, J.W., see Quijada, M.A. 269

Lynn, J.W., see Vasiliu-Doloc, L. 299, 318, 321 Lyon, W.G. 154, 157, 162–164, 166 Lyutsarev, V.S., see Spiridonov, V.P. 227 Lyzlov, Y.N. 203–206 Lyzlov, Y.N., see Nisel’son, L.A. 203–205 Lyzlov, Y.N., see Nisel’son, L.N. 236, 238 Ma, L., see Liu, S. 524, 529 Mabbs, R., see Nijegorodov, N. 506 Mac, M. 491 MacCordick, J., see Bouby, M. 506 MacDonald, D.K.C. 302 Macfarlane, R.M., see Oppenländer, A. 522 Machida, A. 336, 338 Machida, A., see Liu, X.J. 299 Machida, A., see Moritomo, Y. 277, 284, 285 Machida, K., see Jiang, J. 479, 483, 494 Machlan, G.R. 214, 215, 221 Mack, J. 474, 498 Mack, N.H., see Bare, W.D. 470, 509 MacLaughlin, D.E., see Heffner, R.H. 298, 325 Madden, P.A., see Hutchinson, F. 179 Madic, C., see Billard, I. 470, 495, 501–503, 506 Madic, C., see Scapolan, S. 508 Maekawa, S., see Endoh, Y. 315 Maekawa, S., see Ishihara, E. 269 Maekawa, S., see Saitoh, E. 269 Magerramov, E.V., see Aliev, O.M. 55, 80 Mahan, G. 28 Mahan, G.D. 28 Mahan, G.D., see Sofo, J.O. 6 Mahesh, R. 329 Mahia, J., see Platas, C. 358, 359, 377, 378, 400–404 Mahl, S., see Slebarski, A. 45, 59, 60, 100, 113 Maignan, A., see Autret, C. 338 Maignan, A., see Damay, F. 330, 336 Mais, J., see Chmaissem, O. 278, 280 Majumdar, A.K., see Kumar, D. 326 Mak, C.S.K. 525, 581 Makhmadmurodov, A. 195, 239 Makhmadmurodov, A., see Dudchik, G.P. 238 Maksudova, T.F., see Aliev, O.M. 77, 78, 91, 92 Maksudova, T.F., see Rustamov, P.G. 92 Maldivi, P., see Adamo, C. 183, 186–189 Malefetse, T.J., see Swiegers, G.F. 355, 393 Malik, S.K. 48, 56, 60, 69, 77, 81, 85, 89, 108, 118 Malik, S.K., see Adroja, D.T. 60, 61, 118 Malik, S.K., see Mehta, A. 69 Malik, S.K., see Menon Latica 48, 56, 61, 69 Malik, S.K., see Vijaya Lakshmi, K. 121, 124

AUTHOR INDEX Malik, S.R. 95 Malkin, B.Z., see Kupchikov, A.K. 525, 581, 582 Malley, M.F., see Chang, C.A. 420 Malrezzi, A.L., see Dagotto, E. 261 Mal’tsev, A.A., see Loktyushina, N.S. 186, 229–231 Mal’tsev, A.A., see Selivanov, G.K. 186, 189, 227 Mandal, P. 312 Mandal, T.K., see Zhao, Y.G. 328 Mandrus, D., see Bauer, E.D. 13, 16 Mandrus, D., see Chakoumakos, B.C. 8 Mandrus, D., see Feldman, J.L. 11 Mandrus, D., see Gajewski, D.A. 13 Mandrus, D., see Keppens, V. 11 Mandrus, D., see Sales, B.C. 2, 7, 9–11, 13, 26, 29, 31 Manet, I., see Ulrich, G. 358 Mao, H.K. 518 Mao, H.K., see Bell, P.M. 519 Maple, M.B. 22 Maple, M.B., see Bauer, E.D. 8, 12, 13, 15–17, 21, 22, 24 Maple, M.B., see Dilley, N.R. 15, 26 Maple, M.B., see Dordevic, S.V. 8, 12, 17, 26, 27 Maple, M.B., see Gajewski, D.A. 13 Maple, M.B., see Keppens, V. 11 Maple, M.B., see Meisner, G.P. 6, 12 Maple, M.B., see Torikachvili, M.S. 6, 8, 17, 22 Maquina, C., see De Teresa, J.M. 300 Mar, A., see Bollore, G. 43, 47, 49, 50, 55, 57, 58, 60, 62, 69, 71, 72, 74, 75, 110 Mar, A., see Deakin, L. 133 Mar, A., see Ferguson, M.J. 43, 47–50, 57, 58, 61–63, 70, 72, 75, 79, 82, 84, 102, 103 Mar, A., see Lam, R. 47, 55, 60, 68, 74, 78, 80, 83, 84, 103 Mar, A., see Mills, A.M. 47, 54, 60, 68, 74, 104, 111 Mar, A., see Raju, N.P. 43 Mar, R.W. 234 Marazza, R. 41, 48, 56, 61, 69, 74, 81, 83, 85, 87, 88, 91, 106 Marazza, R., see Riani, P. 41, 85, 87, 88, 91, 93 Marazza, R., see Rossi, D. 49, 57, 71, 76 Marcantonatos, M.D. 497, 498 Marcantonatos, M.D., see Deschaux, M. 498 Marcenat, C., see Fisher, R.A. 326 Marcenat, C., see Gordon, J.E. 326 Marchand, R. 76, 79 Marest, G., see Hannoyer, B. 325 Marezio, M., see Cox, D.E. 291

615

Marezio, M., see Hwang, H.Y. 290, 291 Marezio, M., see Radaelli, P.G. 299, 323, 325, 327, 329 Margrave, J.L., see Besenbuch, G. 235 Margrave, J.L., see Charlu, T.V. 164, 165 Margrave, J.L., see Hastie, J.W. 186, 191, 193, 197, 224, 225, 236, 237 Margrave, J.L., see Hauge, R.H. 186, 225, 226 Margrave, J.L., see Kent, R.A. 234 Margrave, J.L., see Zmbov, K.F. 234, 235 Mariani, P., see Bianchi, A. 426 Mariet, C., see Billard, I. 510 Markovich, V. 287, 325 Markovich, V., see Yuzhelevski, Y. 326 Marochko, O.Y., see Solomonik, V.G. 186 Marqina, C., see De Teresa, J.M. 298 Marques, M.P.M. 421, 423 Marques, M.P.M., see Aime, S. 421, 422 Marques, M.P.M., see Geraldes, C.F.G.C. 410 Marquina, C., see De Teresa, J.M. 299 Marsel, J., see Kaposi, O. 196, 240 Martell, A.E. 381 Mårtensson, N., see Johansson, B. 199 Martin, C., see Autret, C. 338 Martin, C., see Damay, F. 330, 336 Martin, I.R., see Lavin, V. 522, 523 Martin, M.C. 322 Martin, R.B., see Bleaney, B. 357, 365, 371 Martin, R.B., see Donato, H. 404 Martin-Mayor, V., see Burgy, J. 332 Martinchuk, E.L., see Kobzenko, G.F. 36 Martínez, B. 317 Martínez, B., see Senis, R. 317 Martínez, B., see Skumryev, V. 312 Martínez, J.L., see Alonso, J. 324 Martínez, J.L., see Fernández-Díaz, M.T. 329 Martinho, H., see Granado, E. 284 Martynova, L.F., see Slovyanskikh, V.K. 94, 95, 140 Marx, A., see Reutler, P. 326 Marx, V., see Petzel, T. 234, 235 Marysko, M., see Jirák, Z. 275 Marysko, M., see Krupicka, S. 330, 338 Masaki, M., see Katsufuji, T. 275 Mason, D.R., see Morrison, C. 530 Massalski, T.B. 36 Masuda, T.D., see Aoki, Y. 17–19 Matachescu, C., see Latva, M. 494, 495 Matacotta, F.C., see Dediu, V. 327 Mathews, C.K., see Peter, S. 507 Mathieu, C.E., see Blair, S. 509

616

AUTHOR INDEX

Mathieu, C.E., see Clarkson, I.M. 484, 505 Mathis, G., see Bazin, H. 509 Mathur, J.N., see Lis, S. 478, 481, 494, 496 Matsuda, T., see Sato, H. 6, 8, 12, 17, 18, 22, 23 Matsuda, T.D. 17 Matsuda, T.D., see Keller, L. 17, 23 Matsuda, T.D., see Sugawara, H. 18 Matsuhata, H., see Lee, C.H. 20 Matsuhira, K. 20 Matsuhira, K., see Sekine, C. 15, 25, 26 Matsui, Y., see Li, J.Q. 329 Matsumoto, A. 506 Matsumoto, G. 275, 324 Matsumoto, G.H. 264 Matsumoto, T., see Naka, T. 521 Matsumoto, T., see Shirotani, I. 9, 10 Matsushita, A., see Shirotani, I. 9, 10 Mat’tsev, A., see Perov, P.A. 186, 227, 228 Mauchien, P., see Berthoud, T. 507, 508 Mauchien, P., see Decambox, P. 507, 508 Mauchien, P., see Moulin, C. 507, 508 Mauchien, P., see Thouvenot, P. 507 Mauger, A., see Ravot, D. 10, 11, 13 Max, J.J. 482 Mayr, F. 315 Mayr, M. 326 Mayr, M., see Burgy, J. 332 Mazin, I.I., see Feldman, J.L. 11 Mazzanti, M., see Bretonnière, Y. 393 Mazzone, D., see Borsese, A. 36 Mazzone, D., see Riani, P. 41, 85, 87, 88, 91 Mazzone, D., see Rossi, D. 49, 57, 71, 76 McCarroll, W.H., see Markovich, V. 287 McClellan, K.J., see Granado, E. 329 McCreary, J.R. 234, 235 McDonald, J.D., see Kent, R.A. 234 McDonald, R., see Lam, R. 47, 60, 68, 74, 80, 83, 84, 103 McElfresh, M.W., see Torikachvili, M.S. 6, 8, 17, 22 McGarvey, B.R. 357, 371, 372, 376, 459 McGreevy, R., see Kusters, R.M. 290 McIlroy, D.N. 295 McIntyre, G.J., see Campbell, A.J. 319 McMasters, D.D., see Schmidt, F.A. 36 McMeeking, R.F., see Gerloch, M. 368 McMurry, T.J., see Caravan, P. 357, 360–362 McNiff Jr., E.J., see Xiao, G. 328 McQueeney, R.J., see Egami, T. 263 McWhan, D.B., see Vettier, C. 521, 535 McWhorter, A.L., see Oliver, M.R. 252

Medarde, M., see Pinsard-Gaudart, L. 268, 280 Medvedev, V.A., see Cox, J.D. 173 Mee, J.E. 208 Mehta, A. 69 Meiboom, S. 363 Meingast, C., see Gordon, J.E. 326 Meinrath, G. 494, 495, 497, 501 Meinrath, G., see Billard, I. 470, 495, 501–503, 506 Meinrath, G., see Nitzsche, O. 506 Meisner, G.P. 6, 8, 9, 11, 12, 20 Meisner, G.P., see Chen, B. 13 Meisner, G.P., see Delong, L.E. 6, 8, 9 Meisner, G.P., see Fleurial, J.-P. 3, 11, 13, 27, 29 Meisner, G.P., see Grandjean, F. 13 Meisner, G.P., see Long, G.J. 13 Meisner, G.P., see Morelli, D.T. 11, 13, 29 Meisner, G.P., see Nolas, G.S. 11 Meisner, G.P., see Shenoy, G.K. 8 Meisner, G.P., see Torikachvili, M.S. 6, 8, 17, 22 Meister, G.E., see Holz, R.C. 474, 482 Meneghini, C. 325 Menon Latica 48, 56, 61, 69 Menon Latica, see Malik, S.R. 95 Menon Latica, see Vijaya Lakshmi, K. 121, 124 Menovsky, A.A., see Fäth, M. 298 Mentink, S.A.M. 54 Menyuk, N., see Goodenough, J.B. 265, 267, 269, 270 Merbach, A.E., see Aime, S. 421, 422 Merbach, A.E., see Hedinger, R. 454 Merbach, A.E., see Marques, M.P.M. 421, 423 Merbach, A.E., see Powell, D.H. 361 Merbach, A.E., see Ruloff, R. 363 Merbach, A.E., see Toth, E. 363, 454 Merkel, B., see Nitzsche, O. 506 Merkle, L.D. 522, 572–574 Merli, L. 174, 210, 213, 216, 220–222 Merlo, F. 91, 92 Mesmer, R.E., see Dai, S. 494 Mesot, J. 524, 535 Metcalf, D.H. 489 Metcalf, D.H., see Hopkins, T.A. 369, 377, 381, 383, 400, 405, 410 Mewis, A., see Dunner, J. 77, 95 Mewis, A., see Klüfers, P. 77, 91 Mewis, A., see Wenski, G. 62, 71, 78, 107 Meyer, D., see Dubost, J.P. 420 Meyer, G. 149 Meyer Jr., E.F., see Kasuga, K. 440 Mezei, F., see Heffner, R.H. 298

AUTHOR INDEX Michael, K. 519 Michel, C., see Chechersky, V. 298 Michels, G., see Dunner, J. 77, 95 Michor, H., see Bauer, E. 24 Miéville, L., see Worledge, W.C. 323 Migliori, A., see Dilley, N.R. 26 Miguel, M., see Rykov, S. 497 Miguel, M.G. 498 Miguel, M.G., see Azenha, M.E. 498 Miguel, M.G., see Burrows, H.D. 497 Mikhailova, N.P., see Savin, V.D. 222 Mikhalsky, Ja.F., see Skolozdra, R.V. 52, 112, 113, 117, 120–123 Milia, F., see Papavassiliou, G. 328 Milicic-Tang, A., see Bünzli, J.-C.G. 493 Millange, F. 336 Millange, F., see Dupont, F. 336 Miller, A.G., see Brina, R. 507 Miller, C.F., see Spedding, F.H. 174, 211, 213 Miller, J., see Sharp, R. 359 Miller, M., see Hilpert, K. 239 Miller, M., see Kapala, J. 190, 191, 193, 232, 233, 236, 237 Millet, O., see Pons, M. 380, 405 Millis, A.J. 17, 26, 268 Millis, A.J., see Ahn, K.H. 267, 268 Millis, A.J., see Quijada, M.A. 296 Mills, A.M. 47, 54, 60, 68, 74, 104, 111 Minai, Y., see Takahashi, K. 481 Minami, A., see Katoh, K. 118 Minomura, S., see Hogg, R.A. 524, 555 Minomura, S., see Takarabe, K. 524, 525, 578–580 Mira, J. 295, 310 Mira, J., see Rivadulla, F. 305 Mirkin, C.A., see Holliday, B.J. 355 Mironov, K.E., see Abdusalamova, M.N. 36, 37, 135 Mironov, V.S. 355, 366, 368–372 Mirov, S., see Hua, H. 521, 522 Mishimura, G. 557 Misumi, M., see Kim, Y.C. 219 Mitchell, J.F., see Louca, D. 304 Mitchell, J.F., see Romero, D.B. 268 Mitchell, J.F., see Roy, M. 291, 328 Mitsuda, S., see Okayama, Y. 521 Mitsuda, S., see Oohara, Y. 521 Mitsuda, S., see Yoshizawa, H. 521 Miyano, K. 291 Miyano, K., see Fiebig, M. 291 Miyano, K., see Ogawa, K. 291 Miyano, Y., see Fiebig, M.K. 291

617

Mizokawa, T. 263 Mizushima, T., see Hogg, R.A. 524, 555 Mizushima, T., see Takarabe, K. 524, 578–580 Mobilio, S., see Meneghini, C. 325 Mochinaga, J., see Igarashi, K. 203–205 Mody, T.D., see Lisowski, J. 357, 358, 364, 374–376 Møller, C. 148 Moller, M.H., see Brylak, M. 42, 48, 56, 61, 69, 75, 81, 83, 85, 87, 89, 90 Moller, M.H., see Jeitschko, W. 15, 23, 24 Molnár, J. 185, 186, 190, 191, 230–232 Molodkin, A.K. 208 Moloney, J.M., see Aime, S. 426, 429 Molski, A. 489, 502 Monaenkova, A.S. 218 Monaenkova, A.S., see Popova, A.A. 213 Monaenkova, A.S., see Tiﬂova, L.A. 216 Monsallier, J.M. 506 Monteil, A. 524, 556 Montgomery, R.L. 210, 211, 214, 219 Mooney, W. 497 Moorman, J., see Spedding, F.H. 164, 165, 176, 178 Morelli, D.T. 11, 13, 29 Morelli, D.T., see Chen, B. 13 Morelli, D.T., see Fleurial, J.-P. 3, 11, 13, 27, 29 Morelli, D.T., see Grandjean, F. 13 Morelli, D.T., see Long, G.J. 13 Morelli, D.T., see Meisner, G.P. 11 Morelli, D.T., see Nolas, G.S. 3, 11, 27 Moreno, N.O., see Granado, E. 284, 329 Moreo, A., see Burgy, J. 332 Moreo, A., see Mayr, M. 326 Moreo, A.M., see Dagotto, E. 261 Moret, E., see Bünzli, J.-C.G. 496 Morgan, L.O., see Bloembergen, N. 356, 359 Morgantini, P.-Y., see Ouali, N. 379, 390, 405–410 Morgenstern, A., see Oppermann, H. 210 Morgenstern, M. 506 Mori, N., see Kohgi, M. 521 Mori, N., see Naka, T. 521 Mori, N., see Okayama, Y. 521 Mori, N., see Oohara, Y. 521 Mori, N., see Yoshizawa, H. 521 Mori, S. 328–330 Mori, S., see Katsufuji, T. 275 Mori, S., see Machida, A. 336 Mori, S., see Uehara, M. 327 Moriarity, J.L. 194, 236–238 Morita, M., see Buddhudu, S. 484

618

AUTHOR INDEX

Moritomo, Y. 277, 284, 285, 291, 311, 326 Moritomo, Y., see Asamitsu, A. 319 Moritomo, Y., see Katsufuji, T. 275 Moritomo, Y., see Kuwahara, H. 333, 337 Moritomo, Y., see Liu, X.J. 299 Moritomo, Y., see Machida, A. 336, 338 Moritomo, Y., see Martin, M.C. 322 Moritomo, Y., see Romero, D.B. 268 Moritomo, Y., see Tokura, Y. 330, 341 Moritomo, Y., see Tomioka, Y. 291 Moritomo, Y., see Urushibara, A. 311 Moriya, T. 258 Moriyasu, M. 489, 491, 504 Moriyasu, M., see Yokoyama, Y. 491, 497 Morozkin, A.V. 40, 81, 83–85, 87–89, 93, 108 Morozova, V.A., see Savin, V.D. 222 Morrison, C. 530 Morrison, C.A. 154, 160–162, 167, 371 Morrison, C.A., see Chang, N.C. 538 Morrison, H.G. 151, 205 Morrison, M.E. 489 Morrison, T.I., see Suib, S.L. 481 Morrow, J.R. 426 Morrow, J.R., see Amin, S. 426 Morss, L.R. 171, 210, 214, 217–222, 467 Morss, L.R., see Fuger, J. 219, 220 Morss, L.R., see Katz, J.J. 467, 500 Moser, M., see Stapor, A. 525, 578 Moshchalkov, V.V., see Aliev, F.G. 118 Moshchalkov, V.V., see Gordon, I. 326 Mosquera, M., see Al-Souﬁ, W. 471, 498 Moss, G.P., see Briggs, J.M. 368, 455 Motalov, V.B., see Kudin, L.S. 193, 237 Motalov, V.B., see Pogrebnoi, A.M. 193, 194, 236, 237 Motokawa, M., see Nojiri, H. 317 Mott, N.F. 260 Moudden, A.H., see Rodríguez-Carvajal, J. 263, 275 Moudden, A.H., see Vasiliu-Doloc, L. 299, 318 Moulin, C. 501, 507, 508 Moulin, C., see Berthoud, T. 507, 508 Moulin, C., see Billard, I. 470, 495, 501–503, 506 Moulin, C., see Couston, L. 499 Moulin, C., see Decambox, P. 507, 508 Moulin, C., see Scapolan, S. 508 Moulin, C., see Thouvenot, P. 507 Moulin, V., see Moulin, C. 501 Moune, O.K., see Faucher, M.D. 550 Moussa, F. 324 Moussa, F., see Biotteau, G. 325 Moussa, F., see Hennion, M. 311, 324

Moussa, F., see Rodríguez-Carvajal, J. 263, 275 Moussavi, M. 440 Moutiers, G., see Billard, I. 510 Mozharivskyj, Yu. 37, 41, 42, 80–90, 92, 93, 111, 138, 139 Mudryi, S.I., see Salamakha, P. 47, 54, 91, 98, 102 Mukhin, A.A., see Mayr, F. 315 Mukkala, V.M., see Hemmilä, I. 509 Mukkala, V.M., see Latva, M. 494, 495 Mukovskii, Y.M., see Adams, C.P. 298 Mukovskii, Y.M., see Biotteau, G. 325 Mukovskii, Y.M., see Quijada, M.A. 269 Mukovskii, Y.M., see Senis, R. 317 Mukovskii, Y.M., see Skumryev, V. 312 Mukovskii, Y.M., see Smolyaninova, V.N. 321 Mukovskii, Y.M., see Vasiliu-Doloc, L. 321 Mukovskii, Ya.M., see Markovich, V. 325 Mukovskii, Ya.M., see Yuzhelevski, Y. 326 Müller, H., see Trommer, R. 578 Müller, K.A., see Zhao, G.-M. 305, 307 Müller, M., see Grund, I. 40, 42, 96 Muller, R.N., see Ruloff, R. 363 Muller, U. 5 Muñoz, J.S., see Skumryev, V. 312 Munro, R.G., see Fujishiro, I. 519 Murakami, S., see Buddhudu, S. 484 Murakami, Y. 263 Murakami, Y., see Endoh, Y. 315 Murakami, Y., see Zimmermann, M.V. 264 Murani, A.P., see Guzik, A. 54 Murata, S., see Tachiya, M. 489 Muravjova, A.A. 43, 137 Murray, G.M., see Del Cul, G.D. 523 Murray, G.M., see Jenkins, A.L. 507 Mustafayev, F.M., see Geydarova, E.N. 85 Mutka, H., see Mesot, J. 524, 535 Muzet, N., see Berny, F. 358 Mydosh, J.A. 270 Mydosh, J.A., see Fäth, M. 298 Mydosh, J.A., see Mentink, S.A.M. 54 Myers, C.E. 182, 184, 186, 192, 194, 237 Myers, C.E., see Hannay, M.H. 236 Nabialek, A., see Troyanchuk, O.Ya. 275 Nachtrieb, N.D., see Jamieson, J.C. 516 Nafziger, R.H. 200 Nagaev, E.L. 293, 305, 307 Nagaishi, R. 497 Nagaishi, R., see Billard, I. 470, 495, 501–503, 506 Nagaishi, R., see Kimura, T. 471–473, 479

AUTHOR INDEX Nagarajan, R., see Patil, S. 53, 80, 133 Naka, T. 521 Nakamura, A., see Liu, X.J. 299 Nakamura, A., see Machida, A. 336, 338 Nakanishi, T., see Shirotani, I. 9, 10 Nakao, H., see Zimmermann, M.V. 264 Nakazawa, Y., see Shirotani, I. 7, 9, 21 Nakazawa, Y., see Uchiumi, T. 7–9, 12 Naler, S. 328 Namiki, T., see Aoki, Y. 17–19 Nanba, T. 20 Narayan, J., see Kumar, D. 326 Nardone, M., see Congeduti, A. 325 Nash, K.L. 493 Natali, F., see Lanzara, A. 295, 325 Nath, A. 325 Nath, A., see Chechersky, V. 295, 296, 298, 305, 325 Naumov, V.A., see Akishin, P.A. 224 Nave, S.E., see Del Cul, G.D. 523 Neck, V., see Fanghänel, T. 500 Nedyak, S., see Perov, P.A. 186, 227, 228 Nehlig, A. 473, 474, 482, 485 Neikirk, D.P., see Powell, R.C. 572 Neilo, G.N., see Krygin, I.M. 521, 522, 536 Neilo, G.N., see Lukin, S.N. 524, 536 Nelson, C.S., see Zimmermann, M.V. 264 Nesmeyanov, A.N. 236 Nessel, F., see Bungenstock, C. 540 Neuenschwander, J. 522, 523, 525 Neuhaus, A. 558 Neumann, H., see Klüfers, P. 77, 91 Neumann, M., see Slebarski, A. 45, 59, 60, 100, 113 Neumeier, J.J. 278, 283, 299 Neumeier, J.J., see Granado, E. 263, 284, 329 Newman, D.J. 530, 531, 542, 545 Newman, D.J., see Bishton, S.S. 547 Newman, D.J., see Bradbury, M.I. 541 Newman, D.J., see Curtis, M.M. 544 Newman, D.J., see Poon, Y.M. 560 Newman, D.J., see Reid, M.F. 547 Ng, B., see Newman, D.J. 530, 542, 545 Ni, B., see Bauer, E. 24 Ni Dhubhghaill, O.M., see Powell, D.H. 361 Niarchos, D., see Kallias, G. 328 Niarchos, D., see Papavassiliou, G. 325, 328 Nibler, J.W., see Lesiecki, M. 186, 224 Nicastro, G., see Bertini, I. 357, 361 Nicholson, A.J.C., see Ciach, S. 236, 237

619

Nickel, H., see Gietmann, C. 194, 196, 197, 207, 209, 238–240 Nickle, S.K., see Cacheris, W.P. 410 Niemann, U., see Hilpert, K. 149 Niemöller, T., see Uhlenbruch, S. 317 Nieuwenhuys, G.J., see Heffner, R.H. 298, 325 Nieuwenhuys, G.J., see Mentink, S.A.M. 54 Nigam, A.K., see Vijaya Lakshmi, K. 121, 124 Nijegorodov, N. 506 Nisel’son, L.A. 203–205 Nisel’son, L.N. 236, 238 Nisel’son, L.N., see Lyzlov, Y.N. 203–206 Nishibori, E., see Machida, A. 336 Nishibori, E., see Moritomo, Y. 277, 284, 285 Nishimura, G. 524 Nishizawa, A., see Endoh, Y. 315 Nitsche, H., see Bernhard, G. 495 Nitsche, H., see Brendler, V. 499 Nitsche, H., see Geipel, G. 495, 499, 500, 505 Nitsche, H., see Rutsch, M. 501 Nitzsche, O. 506 Niu, X.J. 82 Niwa, K., see Shimazaki, E. 206–208, 236, 238–240 Noack, R.A. 518 Noakes, D.R., see Shenoy, G.K. 8 Noël, H., see Flandorfer, H. 127 Noël, H., see Sologub, O. 41, 42, 45, 46, 48, 49, 52, 53, 56, 58–62, 66, 67, 69, 72–76, 79–93, 102, 119–123 Noël, H., see Weitzer, F. 44, 59, 65, 73 Nogués, J., see Skumryev, V. 312 Noh, T.W., see Dho, J. 325 Noh, T.W., see Jung, J.H. 323 Noh, T.W., see Kim, K.H. 296, 328 Nohdo, S., see Yamada, Y. 315 Nojiri, H. 317 Nojiri, H., see Endoh, Y. 315 Nojiri, S., see Sugawara, H. 18 Nolas, G.S. 3, 11, 27–30 Nomura, K., see Chechersky, V. 295, 296, 325 Nordstrom, L. 6, 12, 13 North, A.C.T., see Barry, C.D. 363 Noubactep, C., see Meinrath, G. 495, 497, 501 Novák, P., see Krupicka, S. 338 Novák, P., see Savosta, M.M. 310 Novikov, G., see Suvorov, A.V. 234 Novikov, G.I. 236 Novikov, G.I., see Dudchik, G.P. 236–238 Novikov, G.I., see Polyachenok, O.G. 213, 236, 237

620

AUTHOR INDEX

Novo, M., see Al-Souﬁ, W. 471, 498 Novoselova, A.V., see Shaimuradov, I.B. 202 Novotný, P., see Söhnel, O. 173 Nowitzke, G., see Bungenstock, C. 540 Nozar, P., see Dediu, V. 327 Nozawa, K., see Shirotani, I. 7–9, 12 Nozawa, S., see Kanai, K. 13 Nunes, L.H.A., see De Sa, G.F. 471, 483 Nuñez-Reguero, M., see Meneghini, C. 325 Nunziante Cesaro, S., see Kapala, J. 190, 191, 193, 232, 233, 236, 237 Obradors, X., see Causa, M.T. 326 Obradors, X., see Fontcuberta, J. 299 Obradors, X., see Laukhin, V. 299 Obradors, X., see Senis, R. 317 Obriot, J., see Monteil, A. 524, 556 Oetting, F.L., see Fuger, J. 171 Ofelt, G.S. 560 Offen, H.W., see Gleason, J.K. 524, 551, 566, 568 Oftedal, I. 2 Ogale, S.B., see Hannoyer, B. 325 Ogale, S.B., see Saraf, L.V. 309 Ogale, S.B., see Zhao, Y.G. 328 Ogale, S.B., see Zhao, Y.G. 296 Ogawa, K. 291 Oguro, I., see Katoh, K. 118 Ohara, Y., see Kohgi, M. 521 Ohara, Y., see Okayama, Y. 521 O’Hare, P.A.G., see Flotow, H.E. 154, 157 Ohashi, M., see Kajimoto, R. 337 Ohnishi, T., see Hasegawa, Y. 479, 480 Ohno, K., see Shirotani, I. 7, 9, 10, 21 Ohno, S.I., see Lee, K.P. 492 Ohno, T., see Chahara, K.I. 290 Ohoyama, K., see Kajimoto, R. 337 Ohoyama, K., see Machida, A. 336, 338 Ohshiden, S., see Fujishiro, H. 276 Ohta, T., see Lee, C.H. 20 Oikawa, K., see Yamada, Y. 315 Oishi, J., see Kim, Y.C. 213–215, 217, 219–221 Okada, H., see Matsuda, T.D. 17 Okada, H., see Sato, H. 6, 8, 12, 17, 18, 22, 23 Okako, N., see Iwadate, Y. 179 Okamoto, H., see Massalski, T.B. 36 Okamoto, H., see Villars, P. 37 Okamoto, M., see Tanaka, F. 491, 492 Okamoto, S., see Endoh, Y. 315 Okamoto, S., see Saitoh, E. 269 Okayama, Y. 521 Okayama, Y., see Kohgi, M. 521

Okayama, Y., see Naka, T. 521 Okayama, Y., see Oohara, Y. 521 Okayama, Y., see Yoshizawa, H. 521 Okimoto, Y., see Kimura, T. 336 Okimoto, Y., see Saitoh, E. 321 Okimoto, Y., see Tobe, K. 266, 269 Okuda, T. 325 Olenyuk, B., see Leininger, S. 355 Ole´s, A., see André, G. 123 Oliver, M.R. 252 Olmstead, M.M., see Chan, J.Y. 37, 90 Olsen, L.R. 523 Olsen, L.R., see Wright, A.O. 523, 524 Omenetto, N., see Eliet, V. 474, 498 Onellion, M., see Ren, Y.H. 326 Onuki, Y., see Sugawara, H. 8, 9, 18, 23 Oohara, Y. 521 Oohara, Y., see Yoshizawa, H. 521 Oppenländer, A. 522 Oppermann, H. 210 Oppermann, H., see Hennig, C. 213–215 Ortolani, M., see Meneghini, C. 325 Osakabe, T., see Kasaya, M. 131, 132 Osakabe, T., see Kohgi, M. 521 Osakabe, T., see Okayama, Y. 521 Osakabe, T., see Oohara, Y. 521 Osakabe, T., see Yoshizawa, H. 521 Osborne, D.W., see Lyon, W.G. 154, 157, 162–164, 166 Oseroff, S.B., see Causa, M.T. 326 Oseroff, S.B., see Granado, E. 263, 284, 329 Oshchepkov, D.I., see Laptev, D.M. 216 Osin, S.B., see Loktyushina, N.S. 186, 228, 229 Ott, H.R. 55 Ott, H.R., see Hulliger, F. 48, 49, 78, 94 Ouali, N. 379, 390, 405–410 Ouali, N., see Bocquet, B. 453, 455, 456 Ouali, N., see Floquet, S. 453, 455–459 Ovander, L.N., see Voloshin, V.A. 522, 531 Overend, N. 303 Oyanagi, H., see Lee, C.H. 20 Ozawa, T.C., see Fisher, I.R. 90, 91, 134, 135, 137 Padhan, P., see Srivastava, S. 291, 292 Paetzold, H.K. 516, 521 Palmetshofer, L., see Jantsch, W. 525, 580 Palmetshofer, L., see Przybylinska, H. 525, 580 Panagiotopoulos, I., see Papavassiliou, G. 325 Panak, P. 494, 495 Panak, P., see Klenze, R. 500 Panczer, G., see Gaft, M. 480

AUTHOR INDEX Pandey, N., see Srivastava, S. 291, 292 Pani, M., see Merlo, F. 91, 92 Panigrahi, B.S., see Peter, S. 507 Pankevich, Yu.V. 52, 59, 66, 73 Pankevich, Yu.V., see Pecharsky, V.K. 40, 52, 53, 59, 66, 67, 73, 79, 82, 84, 86, 88, 89, 92, 100, 106, 109, 138, 139 Paoli, P., see Bianchi, A. 426 Papatheodorou, G.N., see Boghosian, S. 184 Papavassiliou, G. 325, 326, 328 Pappalardo, R., see Jørgensen, C.K. 541 Paraskevopoulos, M., see Mayr, F. 315 Parigi, G., see Bertini, I. 362, 363, 367 Parisi, F., see Freitas, R.S. 328, 329 Parisi, F., see Levy, P. 328 Park, K.S., see Lee, K.P. 492 Park, Y.Y. 489, 491, 492, 498 Park, Y.Y., see Yamamura, T. 492 Parker, D. 355, 420, 484, 491, 493, 494, 509 Parker, D., see Aime, S. 426, 429 Parker, D., see Beeby, A. 481–484 Parker, D., see Billard, I. 470, 495, 501–503, 506 Parker, D., see Blair, S. 509 Parker, D., see Bruce, J.I. 355 Parker, D., see Clarkson, I.M. 484, 505 Parker, D., see Dickins, R.S. 481, 482 Parker, V.B. 173 Parker, V.B., see Fuger, J. 171 Parma, L., see Eliet, V. 474, 498 Parodi, N., see Borzone, G. 37, 135, 136 Parodi, N., see Cacciamani, G. 135 Pascal, P. 494 Paschke, D., see Jeitschko, W. 15, 23, 24 Pashinkin, A.S. 237 Pashkevich, Yu.G., see Zvyagin, S. 338 Pasternak, M.P., see Loa, I. 268 Pastor, R.C. 150, 201, 202 Patil, S. 53, 56, 80, 133 Patil, S.I., see Hannoyer, B. 325 Patterson, H.H., see Yersin, H. 523, 569, 570 Paul, C., see Bauer, E. 24 Paul, Ch., see Bauer, E. 24 Paul, D.McK., see Campbell, A.J. 319 Paul, D.McK., see Lees, M.R. 291 Paul, D.Mck., see Zvyagin, S. 338 Paulose, P.L., see Patil, S. 53, 56, 80, 133 Paulus, E.F. 430, 433 Paulus, H., see Buchler, J.W. 449, 450 Paviet, P. 500 Paviet, P., see Fanghänel, T. 500 Paviet-Hartmann, P., see Fanghänel, T. 500

621

Pavlyuk, V.V. 78, 82 Pavlyuk, V.V., see Stetskiv, A.O. 55, 109, 111 Pavone, D., see Baker, F.B. 214 Pawlowska, M.M., see Marcantonatos, M.D. 498 Payne, D.A., see Yoon, S. 326 Peacock, R.D., see Bruce, J.I. 355 Peacock, R.D., see Dickins, R.S. 481 Pécaut, J., see Bretonnière, Y. 393 Pecharsky, A.O., see Niu, X.J. 82 Pecharsky, V.K. 40, 45, 52, 53, 59, 66, 67, 73, 79, 82, 84, 86, 88, 89, 92, 98, 100, 106, 109, 138, 139 Pecharsky, V.K., see Adroja, D.T. 60, 61, 118 Pecharsky, V.K., see Niu, X.J. 82 Pecharsky, V.K., see Pankevich, Yu.V. 52, 59, 66, 73 Peck Jr., W.F., see Cava, R.J. 56 Pelipets, O.V., see Giricheva, N.I. 184, 186, 190, 191, 193, 228, 232 Pelleg, J., see Markovich, V. 287 Peng, J.-L., see Lynn, J.W. 299, 325 Peng, J.L., see Erwin, R.W. 325 Peng, J.L., see Huang, Q. 289, 325 Pennell, R.G., see Johnson, G.K. 209, 210, 212, 213, 215–217, 219, 220 Penzkofer, A., see Holzer, W. 506 Pepe, G., see Kasuga, K. 440 Perakis, I.E., see Ren, Y.H. 326 Perdew, J.P. 148 Perebeinos, V. 268 Perebeinos, V., see Allen, P.B. 268, 269 Periasamy, A., see Sharman, K.S. 470 Perov, P.A. 186, 227, 228 Perry, J.J.B., see Bruce, J.I. 355 Peter, S. 507 Peterman, D.R., see Choppin, G.R. 493 Peters, J.A. 356–359, 362, 368, 373, 377, 378, 380–384, 405 Peters, J.A., see Corsi, D.M. 356 Peters, J.A., see Frullano, L. 421 Peterson, J.R. 522, 558, 559 Peterson, J.R., see Chen, G. 522–524, 529, 549, 550, 557, 558 Peterson, J.R., see Daniel, J.F. 151, 205 Peterson, J.R., see Del Cul, G.D. 523, 558 Peterson, J.R., see Haire, R.G. 558 Peterson, J.R., see Morrison, H.G. 151, 205 Peterson, J.R., see Stump, N.A. 523, 557 Peterson, J.R., see Wilmarth, W.R. 521, 522, 558 Peterson, J.R., see Young, J.P. 558 Peterson, R.C., see Kasuga, K. 440 Petkov, V., see Billinge, S.J.L. 304

622

AUTHOR INDEX

Petoud, S. 355, 384–387 Petoud, S., see Bünzli, J.-C.G. 496 Petoud, S., see Piguet, C. 393–395 Petzel, T. 234, 235 Petzel, T., see Greis, O. 559 Pfeiffer, S., see Buchler, J.W. 449 Phelps, D.E., see Vold, R.L. 364 Phillips, N.E., see Fisher, R.A. 326 Phillips, N.E., see Gordon, J.E. 326 Phillips, R., see Stubbleﬁeld, C.T. 215 Phillips, R.F., see Evans, D.F. 356 Piacente, V. 195, 237, 239, 240 Piacente, V., see Brunetti, B. 195, 236–240 Piacente, V., see Villani, A.R. 195, 236, 238–240 Picard, G., see Joubert, L. 182, 183, 187–189 Pichlmaier, M., see Holzer, W. 506 Pickett, W.E., see Singh, D.J. 6 Pieper, M.W., see Allodi, G. 325, 328, 337 Piermarini, G.J. 518, 519 Piermarini, G.J., see Barnett, J.D. 522, 552, 554 Piermarini, G.J., see Fujishiro, I. 519 Pierre, J., see Guzik, A. 54, 113 Pierre, J., see Kaczmarska, K. 80, 112, 113 Pierre, J., see Skolozdra, R.V. 52, 112, 113, 117, 120–123 Pifer, J.H., see Sakai, N. 518 Piguet, C. 355, 356, 384, 385, 393–395 Piguet, C., see Bocquet, B. 453, 455, 456 Piguet, C., see Bünzli, J.-C.G. 355 Piguet, C., see Elhabiri, M. 443–445, 448, 481, 494 Piguet, C., see Floquet, S. 453, 455–459 Piguet, C., see Ouali, N. 379, 390, 405–410 Piguet, C., see Petoud, S. 355, 384–387 Piguet, C., see Platas-Iglesias, C. 406, 407 Piguet, C., see Renaud, F. 387–393, 408 Piguet, C., see Rigault, S. 358, 361, 363, 366, 378, 389, 390, 396–400, 403, 444, 446–448 Pimenov, A., see Mayr, F. 315 Pina, F., see Bazzicalupi, C. 492, 509 Pinkerton, A.A. 357, 365, 366, 415–418 Pinkerton, A.A., see Spiliadis, S. 358, 377, 415 Piñol, S., see Causa, M.T. 326 Pinsard, L., see Allodi, G. 288 Pinsard, L., see Anane, A. 291 Pinsard, L., see Biotteau, G. 325 Pinsard, L., see Cestelli Guidi, M. 264 Pinsard, L., see Hennion, M. 311, 324 Pinsard, L., see Martínez, B. 317 Pinsard, L., see Moussa, F. 324 Pinsard, L., see Rodríguez-Carvajal, J. 263, 275

Pinsard, L., see Skumryev, V. 312 Pinsard, L., see Uhlenbruch, S. 317 Pinsard-Gaudart, L. 268, 280 Pinsard-Gaudart, L., see Daoud-Aladine, M. 328, 335, 336 Pinsard-Gaudart, L., see Klingeler, R. 315 Pissas, M. 329 Pissas, M., see Kallias, G. 328 Pissas, M., see Papavassiliou, G. 325, 328 Pissas, M., see Simopoulos, A. 328 Pizer, K.S., see Lewis, G.N. 182 Plancque, G., see Billard, I. 470, 495, 501–503, 506 Platas, C. 358, 359, 377, 378, 400–404 Platas, C., see Geraldes, C.F.G.C. 358, 378, 404, 405 Platas-Iglesias, C. 406, 407 Platas-Iglesias, C., see Corsi, D.M. 356 Plesset, M.S., see Møller, C. 148 Plummer, E.W., see Dai, P. 325 Podzorov, V. 327 Poeppelmeier, K.R. 282 Poettgen, R., see Gordon, R.A. 56, 95 Pogrebnoi, A.M. 193, 194, 236, 237 Pogrebnoi, A.M., see Kudin, L.S. 193, 237, 238 Poilblanc, D., see Dagotto, E. 261 Polla, G., see Levy, P. 328 Pollert, E., see Jirák, Z. 275 Polyachenok, O.G. 209, 212, 213, 215, 219, 236, 237 Polyachenok, O.G., see Dudchik, G.P. 236–238 Polyachenok, O.G., see Makhmadmurodov, A. 195, 239 Pons, M. 380, 405 Poon, Y.M. 560 Poon, Y.M., see Newman, D.J. 530 Popov, V., see Ilisavskii, Y. 326 Popova, A.A. 213 Popovic, A., see Bencze, L. 186, 226, 235 Popovic, A., see Kaposi, O. 196, 240 Popper, P., see Ruddlesden, S.N. 250 Porsch, F., see Shen, Y.R. 564 Porter, B. 200, 201 Poshevneva, A.I. 182, 208 Poshevneva, A.I., see Goryushkin, V.F. 180, 182, 205, 206, 209, 223 Postorino, P., see Congeduti, A. 325 Pöttgen, R., see Gordon, R.A. 56, 97, 113 Potthast, J., see Petzel, T. 234, 235 Pouliquen, J. 488 Pouyat, D., see Couston, L. 499

AUTHOR INDEX Pouyat, D., see Moulin, C. 508 Powell, D.H. 361 Powell, H., see Marques, M.P.M. 421, 423 Powell, R.C. 572 Powell, R.C., see Merkle, L.D. 522, 572–574 Prado, F., see Causa, M.T. 326 Préaudat, M., see Bazin, H. 509 Prellier, W., see Zhao, G. 326 Prellier, W., see Zhao, G.-M. 308 Prendergast, F.G., see Kemple, M.D. 357, 358, 367, 373–375, 386 Preston, S.R., see Gardner, P.J. 168 Preuss, H., see Dolg, M. 148, 183, 187–189 Prewitt, C.T., see Shannon, R.D. 250 Prince, A., see Villars, P. 37 Prins, L.J. 393 Prior, P., see Chmaissem, O. 278, 280 Proffen, Th., see Billinge, S.J.L. 304 Proietti, M.G., see Subías, G. 323 Prokhorov, A.D., see Krygin, I.M. 521, 522, 536 Prokhorov, A.D., see Lukin, S.N. 524, 536 Protsyk, O. 45, 53 Prudnikov, A.M., see Voloshin, V.A. 522, 531 Pryadun, V.V., see Aliev, F.G. 118 Przybylinska, H. 525, 580 Przybylinska, H., see Jantsch, W. 525, 580 Pubanz, D., see Aime, S. 421, 422 Pubanz, D., see Marques, M.P.M. 421, 423 Pubanz, D., see Powell, D.H. 361 Pubanz, D., see Ruloff, R. 363 Pulukkody, K., see Parker, D. 420 Purcell, F.J., see Kaminski, R. 507 Puzniak, R., see Markovich, V. 325 Pyatkov, V.I., see Lebedev, V.A. 36 Pyles, B., see Chmaissem, O. 278, 280 Pyykkö, P., see Golding, R.M. 357, 371 Qi Li, see Ren, Y.H. 326 Quezel, G., see Quezel, S. 275 Quezel, S. 275 Quezel, S., see Burlet, P. 55 Quezel, S., see Rossat-Mignod, J. 55, 57 Quezel-Ambrunat, S. 275 Quijada, M.A. 269, 296 Raber, D.J., see Peters, J.A. 356–359, 362, 368, 373, 380 Rachmatov, O.I., see Abdusalamova, M.N. 37 Radaelli, P.G. 299, 323, 325, 327, 329 Radaelli, P.G., see Cox, D.E. 291 Radaelli, P.G., see Hwang, H.Y. 290, 291

623

Radaelli, P.G., see Lanzara, A. 295, 325 Radenkovic, B., see Jovani´c, B.R. 522, 524, 563 Radli´nski, A.P. 523, 536 Radousky, H.B., see Yoo, C.S. 522, 549, 550 Rai, D., see Felmy, A.R. 506 Rainford, B.D., see Adroja, D.T. 60, 61, 118 Rainford, B.D., see Thornton, M.J. 124 Rajeswari, M., see Quijada, M. 296 Rajeswari, M., see Zhao, G.-M. 308 Rajeswari, M., see Zhao, Y.G. 296 Rajnak, K., see Carnall, W.T. 383 Raju, A.R., see Joshi, J.P. 336 Raju, N.P. 43 Rakhmatov, O.I., see Abdusalamova, M.N. 36, 37 Rakicioglu, Y. 508 Ramakrishnan, S., see Malik, S.R. 95 Raman, A., see Wang, R. 48, 49, 75 Ramesh, R., see Quijada, M. 296 Ramesh, R., see Saraf, L.V. 309 Ramesh, R., see Zhao, Y.G. 296 Ramirez, A.P., see Cava, R.J. 56 Ramirez, A.P., see Radaelli, P.G. 327 Ramirez, A.P., see Roy, M. 291, 328 Ramirez, A.P., see Schiffer, P. 328 Ramondo, F., see Hilpert, K. 239 Ramos, C., see Rivadulla, F. 321 Ramos, C.A., see Causa, M.T. 326 Ramos, C.A., see Mira, J. 310 Rana, R.S., see Carnall, W.T. 383 Randall, E.W., see Briggs, J.M. 368, 455 Randall, M., see Lewis, G.N. 182 Rao, B.D.N., see Kemple, M.D. 357, 358, 367, 373–375, 386 Rao, C.N.R. 330 Rao, C.N.R., see Joshi, J.P. 336 Raquet, B. 326 Ratcliff II, W., see Heffner, R.H. 325 Ratnikova, I.D., see Sobolev, B.P. 202 Rau, D., see Buddhudu, S. 484 Raveau, B., see Autret, C. 338 Raveau, B., see Damay, F. 330, 336 Ravi Bathe, see Hannoyer, B. 325 Ravot, D. 10, 11, 13, 57 Ravot, D., see Rossat-Mignod, J. 55, 57 Ray, B.D., see Kemple, M.D. 357, 358, 367, 373–375, 386 Raymo, F.M., see Balzani, V. 355 Raymond, K.N., see Wu, S.L. 492 Razavi, F.S., see Casa, D. 315 Rebizant, J., see Spirlet, M.-R. 420 Redwing, J.M., see Culp, T.D. 524, 578, 579

624

AUTHOR INDEX

Reed, T.B., see Oliver, M.R. 252 Reed, W.J., see Allsopp, S.R. 473, 474 Rehr, A. 76, 111 Rehr, A., see Chan, J.Y. 134 Reich, T., see Bernhard, G. 495 Reid, M.F. 547, 561 Reid, M.F., see Jayasankar, C.K. 522, 547 Reid, M.F., see Li, C.L. 547 Reilley, C.N. 357, 376, 377, 404–407, 410, 443 Reilley, C.N., see Bryden, C.C. 376, 410, 471, 478, 505 Reilley, C.N., see Desreux, J.F. 357 Reimann, K., see Stapor, A. 525, 578 Reinhoudt, D., see Steemers, F. 494 Reinhoudt, D.N., see Klink, S.I. 471, 494–496 Reinhoudt, D.N., see Prins, L.J. 393 Reisfeld, R., see Gaft, M. 480 Reisfeld, R., see Jørgensen, C.K. 497, 529 Reiß, G., see Bungenstock, C. 540 Reissner, M., see Leithe-Jasper, A. 26 Reller, A. 282 Ren, J. 358, 420, 423–426, 429–431, 433–440 Ren, J., see Sherry, A.D. 433 Ren, S.Y. 580 Ren, Y.H. 326 Renard, J.-P., see Anane, A. 291 Renaud, F. 387–393, 408 Renaud, F., see Bocquet, B. 453, 455, 456 Renaud, F., see Petoud, S. 355, 384–387 Reppke, M., see Dunner, J. 77, 95 Reshetnikova, L.P., see Shaimuradov, I.B. 202 Rettori, C., see Granado, E. 263, 284, 329 Reuben, J. 358, 365, 376, 377, 379, 380, 436 Reuter, G. 166, 167, 205 Reutler, P. 326 Revcolevschi, A., see Anane, A. 291 Revcolevschi, A., see Biotteau, G. 325 Revcolevschi, A., see Daoud-Aladine, M. 328, 335, 336 Revcolevschi, A., see Hennion, M. 311, 324 Revcolevschi, A., see Klingeler, R. 315 Revcolevschi, A., see Martínez, B. 317 Revcolevschi, A., see Moussa, F. 324 Revcolevschi, A., see Pinsard-Gaudart, L. 268, 280 Revcolevschi, A., see Skumryev, V. 312 Revcolevschi, A., see Uhlenbruch, S. 317 Revcolevschi, A., see Vasiliu-Doloc, L. 299, 318 Revcolevshi, A., see Rodríguez-Carvajal, J. 263, 275 Reversat, L., see Anane, A. 291 Revzin, B., see Markovich, V. 287

Rewaj, T. 523, 524, 536 Rezukhina, T.N. 209, 212 Rezukhina, T.N., see Kholokhova, L.I. 211, 213, 215, 216, 221 Riani, P. 41, 85, 87, 88, 91, 93 Riazance, N., see Nafziger, R.H. 200 Richardson, F. 493 Richardson, F.S., see Burdick, G.W. 548 Richardson, F.S., see Hopkins, T.A. 369, 377, 381, 383, 400, 405, 410 Richardson, F.S., see Metcalf, D.H. 489 Riedener, T., see Shen, Y.R. 525, 575–577 Riedi, P.C., see Thornton, M.J. 124 Riedl, U., see Yersin, H. 569 Riehl, J.P., see Huskowska, E. 405 Rigault, S. 358, 361, 363, 366, 378, 389, 390, 396–400, 403, 444, 446–448 Rigault, S., see Ouali, N. 379, 390, 405–410 Rigault, S., see Piguet, C. 355, 393 Rillo, C., see Stankiewicz, J. 292 Ritter, C., see De Teresa, J.M. 298 Ritter, C., see Frontera, C. 336 Ritter, C., see García-Landa, B. 338 Ritter, C., see Llobet, A. 336 Rivadulla, F. 305, 309, 321, 328, 330–335, 337–342 Rivadulla, F., see Causa, M.T. 326 Rivadulla, F., see Hueso, L.E. 326 Rivadulla, F., see Mira, J. 295, 310 Rivas, J., see Causa, M.T. 326 Rivas, J., see Hueso, L.E. 326 Rivas, J., see Mira, J. 295, 310 Rivas, J., see Rivadulla, F. 305, 309, 321 Rivasibid, J., see Mira, J. 295 Rizkalla, E.N., see Choppin, G.R. 499 Roberts, D.W., see Hawkes, G.E. 368 Roberts, J.A. 192, 197, 234 Roberts, J.D., see Hawkes, G.E. 368 Robinson, M. 200 Robinson, M., see Pastor, R.C. 150, 201, 202 Röder, H., see Heffner, R.H. 298 Röder, H., see Louca, D. 263 Rodewald, U.C., see Jeitschko, W. 15, 23, 24 Rodriguez, V.D., see Lavin, V. 523 Rodriguez-Blas, T., see Geraldes, C.F.G.C. 358, 378, 404, 405 Rodriguez-Blas, T., see Platas, C. 358, 359, 377, 378, 400–404 Rodríguez-Carvajal, J. 263, 275 Rodríguez-Carvajal, J., see Biotteau, G. 325 Rodríguez-Carvajal, J., see Brinks, H.W. 275, 276

AUTHOR INDEX Rodríguez-Carvajal, J., see Daoud-Aladine, M. 328, 335, 336 Rodríguez-Carvajal, J., see Frontera, C. 336 Rodríguez-Carvajal, J., see García-Muñoz, J.L. 323 Rodríguez-Carvajal, J., see Hennion, M. 311, 324 Rodríguez-Carvajal, J., see Moussa, F. 324 Rodríguez-Carvajal, J., see Pinsard-Gaudart, L. 268, 280 Rodriguez-Mendoza, U.R., see Lavin, V. 523 Rodriguez-Ubis, J.C., see Latva, M. 494, 495 Roffe, M. 205 Rogl, P., see Bauer, E. 24 Rogl, P., see Flandorfer, H. 91, 92, 118, 127 Rogl, P., see Leithe-Jasper, A. 26, 43, 44, 51, 52, 59, 63, 64, 66, 72, 73, 79 Rogl, P., see Sologub, O. 41–43, 45–49, 51–54, 56–63, 66–69, 72–76, 79–93, 102, 103, 119–123, 133 Rogl, P., see Weitzer, F. 44, 59, 65, 73 Rohovec, J., see Frullano, L. 421 Rojo, J.M., see Alonso, J. 324 Rome, J.F., see Hirayama, C. 196, 197, 239, 240 Romero, D.B. 268 Roque, A., see Bazzicalupi, C. 492, 509 Rorif, F., see Merli, L. 174, 210, 213, 216, 220–222 Rørmark, L., see Faaland, S. 323 Rosato, A., see Bertini, I. 374 Rose, R.A., see Brink, J.M. 364 Rosenberg, E., see Markovich, V. 287 Rossat-Mignod, J. 55, 57 Rossat-Mignod, J., see Burlet, P. 55 Rossat-Mignod, J., see Quezel, S. 275 Rossat-Mignot, J., see Ravot, D. 57 Rossel, C., see Torikachvili, M.S. 6, 8, 17, 22 Rossi, D. 49, 57, 71, 76 Rossi, D., see Marazza, R. 41, 48, 56, 61, 69, 74, 81, 83, 85, 87, 88, 91, 106 Rossi, P., see Bianchi, A. 426 Rossier, M., see Pinkerton, A.A. 357, 365, 366 Rossini, I., see Bouby, M. 506 Rossotti, F.J.C., see Alsaadi, B.M. 361, 405–407 Roszak, S., see Kapala, J. 190, 191, 193, 232, 233, 236, 237 Roth, K., see Hoeft, S. 421, 422 Roudaut, E., see Quezel, S. 275 Rowe, D.M. 28 Rowe, D.M., see Kuznetsov, V.L. 24, 26 Rowley, A.J., see Hutchinson, F. 179 Roy, M. 291, 328

625

Royle, L., see Beeby, A. 481–484 Rozenberg, E., see Markovich, V. 287, 325 Rozenberg, E., see Yuzhelevski, Y. 326 Rozenberg, G.Kh., see Loa, I. 268 Rozenberg, M.J. 261, 315 Ruani, G., see Dediu, V. 327 Rübhausen, M., see Björnsson, P. 268 Rübhausen, M., see Naler, S. 328 Rubini, P., see Giroux, S. 494, 505 Ruddlesden, S.N. 250 Rudowicz, C., see Tanner, P.A. 557 Rudzitis, E. 215, 219 Ruf, T., see Goncharov, A.F. 522, 582 Rühl, R. 76, 90 Ruloff, R. 363 Runde, W., see Kim, J.I. 496 Ruoff, A.L., see Asaumi, K. 519 Rupprecht, K., see Lübbers, R. 518 Rurack, K. 509 Russavage, E., see Kaminski, R. 507 Rustamov, P.G. 74, 77, 81, 83, 92 Rustamov, P.G., see Aliev, O.M. 55, 77, 78, 80, 91, 92 Rustamov, P.G., see Geidarova, E.A. 42, 71, 75, 85 Rustenholtz, A. 474 Rustenholtz, A., see Billard, I. 485 Rutledge, J.L., see Stubbleﬁeld, C.T. 215 Rutsch, M. 501 Ryan, W., see Ferguson, M.J. 49, 57, 61, 70, 75, 103 Rycerz, L. 166, 168, 179, 180, 204–206, 222, 223 Rycerz, L., see Gaune-Escard, M. 151, 166–168, 179, 203–206, 222, 223 Rykov, S. 497 Ryskin, A.I., see Kupchikov, A.K. 525, 581, 582 Rzaev, D.A., see Kupchikov, A.K. 525, 581, 582 Sabbatini, N. 494 Sabbatini, N., see Balzani, V. 471 Sabbatini, N., see Ulrich, G. 358 Sacco, A. 482 Saccone, A., see Flandorfer, H. 91, 92, 118 Sadygov, F.M. 36, 75 Safaraliev, G.I., see Kuliev, A.N. 74 Saini, N.L., see Lanzara, A. 295, 325 Saito, H., see Sekine, C. 20, 23 Saitoh, E. 269, 321 Sakai, A., see Sekine, C. 20, 23 Sakai, N. 518 Sakai, Y., see Park, Y.Y. 489, 491, 492, 498 Sakaie, K.E. 296

626

AUTHOR INDEX

Sakakibara, T., see Matsuhira, K. 20 Sakakibara, T., see Sekine, C. 15, 20, 25, 26 Sakata, M., see Machida, A. 336 Sakata, M., see Moritomo, Y. 277, 284, 285 Salamakha, P. 47, 54, 56, 66, 91, 98, 102, 109, 138, 139 Salamakha, P., see Protsyk, O. 45, 53 Salamakha, P., see Sologub, O. 62, 63, 65, 67–69, 137 Salamakha, P.S., see Skolozdra, R.V. 41, 46, 53, 59, 60, 67, 73, 80, 82, 84, 86–88, 132, 133 Salamakha, P.S., see Sologub, O.L. 58, 72, 91, 106 Salamakha, P.S., see Zaplatynsky, O.V. 67, 69 Salamon, M.B., see Chun, S.H. 298 Salamon, M.B., see Jaime, M. 300 Salamon, M.B., see Sakaie, K.E. 296 Sales, B.C. 2, 3, 7, 9–11, 13, 26–29, 31 Sales, B.C., see Bauer, E.D. 13, 16 Sales, B.C., see Chakoumakos, B.C. 8 Sales, B.C., see Dilley, N.R. 26 Sales, B.C., see Feldman, J.L. 11 Sales, B.C., see Gajewski, D.A. 13 Sales, B.C., see Keppens, V. 11 Sales, B.C., see Mahan, G. 28 Sales, K.D., see Briggs, J.M. 368, 455 Salmon, P.S., see Hutchinson, F. 179 Salmon, P.S., see Wasse, J.C. 179 Samouël, M., see De Kozak, A. 201 Samsonova, N.D., see Aliev, O.M. 77, 78, 91 Samwer, K., see von Helmolt, R. 290 Sánchez, R.D., see Rivadulla, F. 309, 321 Sandhu, S. 497 Sandmann, C., see Dierolf, V. 525, 529, 555 Sandrok, J., see Seifert, H.J. 204, 205 Sanjurjo, J.A., see Granado, E. 263, 284, 329 Sankar, J., see Kumar, D. 326 Santoro, A., see Huang, Q. 289, 325, 328, 329 Santoro, A., see Lynn, J.W. 299, 325 Santoro, M., see Bungenstock, C. 521, 533 Santosh, P.N., see Rao, C.N.R. 330 Sanygin, V.P., see Slovyanskikh, V.K. 94, 95, 140 Saraf, L.V. 309 Sardar, D., see Powell, R.C. 572 Sarma, D.D., see Congeduti, A. 325 Sarma, D.D., see Meneghini, C. 325 Sarrao, J.L., see Billinge, S.J.L. 304 Sato, H. 6, 8, 12, 17, 18, 22, 23 Sato, H., see Aoki, Y. 17–19 Sato, H., see Keller, L. 17, 23 Sato, H., see Matsuda, T.D. 17 Sato, H., see Sugawara, H. 8, 9, 18, 23

Sato, N., see Kasaya, M. 131, 132 Sato, S. 572 Sato, Y., see Kimura, S. 130 Sato-Sorensen, Y., see Bi, Q. 523, 529, 553 Savin, A., see Dolg, M. 148 Savin, V.D. 222 Savosta, M.M. 310 Savosta, M.M., see Krupicka, S. 338 Savutskii, A.I., see Voloshin, V.A. 523, 524, 571 Sawa, H., see Katoh, K. 118 Sawaki, Y., see Takenaka, K. 321 Sawatzky, G.A., see Mizokawa, T. 263 Sawatzky, G.A., see Zaanen, J. 256, 277 Sazonov, L.A., see Nesmeyanov, A.N. 236 Scanlon, J.C., see Poeppelmeier, K.R. 282 Scapolan, S. 508 Scardala, P., see Brunetti, B. 195, 236–240 Scardala, P., see Piacente, V. 195, 237, 239, 240 Scardala, P., see Villani, A.R. 236, 238, 240 Schaad, O., see Piguet, C. 393–395 Schaefer, M.C.R., see Dubost, J.P. 420 Schaffer, H., see Cordier, G. 43, 44, 46 Scheffold, R., see Löliger, J. 356 Schenk, K.J., see Petoud, S. 355, 384–387 Scherbaum, F., see Billard, I. 470, 495, 501–503, 506 Scherbaum, F.J., see Monsallier, J.M. 506 Schiferl, D., see Hess, N.J. 523, 553 Schiffer, P. 328 Schiffer, P., see Roy, M. 291, 328 Schiffer, P.E., see Radaelli, P.G. 327 Schirber, J.E. 521 Schlaepfer, W., see Powell, D.H. 361 Schmidt, F.A. 36 Schmidt, T. 94, 135, 140 Schmidtke, H., see Jørgensen, C.K. 541 Schneider, A., see Kutscher, J. 208, 209 Schneider, A., see Vogel, G. 203–205 Schneider, M., see Ren, Y.H. 326 Schoenes, J., see Frick, B. 94, 140 Schollerer, G., see Yoon, S. 326 Scholz, F., see Stapor, A. 525, 578 Scholz, U.D., see Evers, C.B.H. 15, 23 Scholz, U.D., see Evers, Ch.B.H. 65, 71, 72, 74, 76, 77, 95 Schröck-Vietor, W., see Hellwege, K.H. 516, 523 Schubert, G., see Fanghänel, T. 500 Schuddinck, W., see Gordon, I. 326 Schulman, S., see Rakicioglu, Y. 508 Schulte, O., see Shen, Y.R. 522 Schultz, L., see von Helmolt, R. 290

AUTHOR INDEX Schuster, H.-U., see Grund, I. 40, 42, 96 Schuster, H.-U., see Klüfers, P. 77, 91 Schuster, H.U., see Fischer, H.O. 49, 58, 62 Schuster, H.U., see Tomuschat, C. 77, 78 Schuurmans, F.J.P. 471, 485 Schwartz, R.W., see Fronczek, F. 381 Schwarz, U., see Loa, I. 268 Schwarzenbach, D., see Pinkerton, A.A. 415 Schwarzenbach, D., see Spiliadis, S. 415 Schweizer, S., see Tröster, Th. 523, 550 Schwenk, H., see Zvyagin, S. 338 Scopelliti, R., see Elhabiri, M. 443–445, 448, 481, 494 Scott, P., see Kaltsoyannis, N. 366 Scully, A.D. 489 Sczepananiak, W., see Gaune-Escard, M. 151, 166–168, 179, 203–206, 222, 223 Seaborg, G.T., see Katz, J.J. 467, 500 Searcy, A.W., see Lim, M. 234 Searcy, A.W., see Mar, R.W. 234 Searcy, A.W., see Roberts, J.A. 192, 197, 234 Searcy, A.W., see Skinner, H.B. 192, 234 Sechovsky, V., see Matsuda, T.D. 17 Seetharaman, S., see Stolyarova, V.L. 235 Seifert, H., see Dudek, H. 206 Seifert, H.J. 203–205 Seifert, H.J., see Büchel, D. 151, 206 Seifert, H.J., see Reuter, G. 166, 167, 205 Seifert, H.J., see Roffe, M. 205 Seifert, H.J., see Thiel, G. 204 Seirania, K.B., see Sobolev, B.P. 150, 200–203 Sekachev, Y.N., see Selivanov, G.K. 186, 189, 227 Sekine, C. 7, 13, 15, 19–21, 23–26 Sekine, C., see Lee, C.H. 20 Sekine, C., see Matsuhira, K. 20 Sekine, C., see Nanba, T. 20 Sekine, C., see Shirotani, I. 7, 9, 10, 13, 21 Sekine, C., see Uchiumi, T. 7–9, 12 Selivanov, G.K. 186, 189, 227 Sémon, L., see Billard, I. 485 Sémon, L., see Rustenholtz, A. 474 Sémon, L., see Simonin, J.P. 491 Senanayake, K., see Clarkson, I.M. 484, 505 Senanayake, P.K., see Blair, S. 509 Senanayake, P.K., see Parker, D. 491, 509 Señaris Rodríguez, M.A., see Mira, J. 310 Senis, R. 317 Senis, R., see Martínez, B. 317 Senis, R., see Skumryev, V. 312 Sesé, J., see Stankiewicz, J. 292

627

Sessler, J.L., see Lisowski, J. 357, 358, 364, 374–376 Sessoli, R., see Hedinger, R. 454 Settai, R., see Sugawara, H. 8, 9, 18, 23 Sevast’yanov, V.G., see Ezhov, Y.S. 230 Shaffer, J., see Dabrowski, B. 311 Shahguliyev, N.S., see Sadygov, F.M. 36 Shahkalamyam, G.S., see Sobolev, B.P. 202 Shaimuradov, I.B. 202 Shaked, H. 84, 87, 89, 90, 127, 129 Shakhkalamian, G.S., see Sobolev, B.P. 150 Shames, A.I. 338 Shames, A.I., see Markovich, V. 325 Shand, W.A., see Jones, D.A. 200–203 Shaner, J.W., see Mao, H.K. 518 Shannon, R.D. 250, 400, 402 Shariﬁ, F., see Hudspeth, H.D. 326 Sharma, P.A., see Kim, K.H. 327 Sharman, K.S. 470 Sharp, J., see Nolas, G.S. 28 Sharp, J.W., see Mahan, G. 28 Sharp, J.W., see Sales, B.C. 11 Sharp, R. 357, 359 Shen, W., see Chi, Y. 523 Shen, Y.R. 518, 522, 523, 525, 529, 533, 534, 541, 542, 544–546, 548, 554, 564–566, 575–577, 581 Shen, Y.R., see Gregorian, T. 521, 522 Shen, Y.R., see Lorenz, B. 522, 554 Shen, Z.X., see Dessau, D.S. 268 Shen, Z.X., see Li, J.-M. 325 Shengalaya, A., see Zhao, G.-M. 305, 307 Shenoy, G.K. 8 Shenoy, G.K., see Suib, S.L. 481 Sherry, A.D. 357, 377, 411–413, 433 Sherry, A.D., see Cacheris, W.P. 410 Sherry, A.D., see Geraldes, C.F.G.C. 358, 378, 404, 405, 410, 411, 414, 415, 417, 418, 420, 424, 425, 427, 429–433, 435–440, 442, 443, 451, 453 Sherry, A.D., see Marques, M.P.M. 421, 423 Sherry, A.D., see Ren, J. 358, 420, 423–426, 429–431, 433–440 Sherry, A.D., see Zhang, S. 355 Shevel’kov, V.F., see Loktyushina, N.S. 186, 228, 229 Shevtsova, Z.N., see Korshunov, B.G. 204 Shimazaki, E. 206–208, 236, 238–240 Shimomura, S. 326, 327 Shin, H. 478 Shin, S., see Kanai, K. 13 Shinno, I., see Gaft, M. 480 Shiokawa, Y., see Matsuda, T.D. 17

628

AUTHOR INDEX

Shiozaki, R., see Takenaka, K. 321 Shirane, G., see Martin, M.C. 322 Shirane, G., see Vettier, C. 521, 535 Shirotani, I. 7–10, 12, 13, 21 Shirotani, I., see Lee, C.H. 20 Shirotani, I., see Matsuhira, K. 20 Shirotani, I., see Nanba, T. 20 Shirotani, I., see Sekine, C. 7, 13, 15, 19–21, 23–26 Shirotani, I., see Uchiumi, T. 7–9, 12 Shishkin, E.A., see Abdusalamova, M.N. 37 Shlykov, S.A., see Girichev, G.V. 229 Shlykov, S.A., see Giricheva, N.I. 184, 186, 190, 191, 193, 227, 228, 232 Shlykov, S.A., see Zakharov, A.V. 184, 186, 190, 191, 195, 229, 232 Short, S., see Dabrowski, B. 311 Shraiman, B.J., see Millis, A.J. 268 Shreekala, R., see Quijada, M. 296 Shreekala, R., see Zhao, Y.G. 296 Shrivastava, K.N. 279, 280 Shteynberg, D.B., see Sobolev, B.P. 150 Shuh, D., see Allen, P. 474 Shulyatev, D., see Biotteau, G. 325 Shulyatev, D.A., see Adams, C.P. 298 Shulyatev, D.A., see Markovich, V. 325 Shulyatev, D.A., see Vasiliu-Doloc, L. 321 Shulyatev, D.A., see Yuzhelevski, Y. 326 Shumakova, T.P., see Abdusalamova, M.N. 37 Siewenie, J.E., see Dabrowski, B. 311, 323 Sikorski, M. 489 Silversmith, A.J., see Radli´nski, A.P. 523, 536 Simon, A., see Gunselius, H. 151 Simoni, E., see Billard, I. 470, 495, 501–503, 506 Simonin, J.P. 488, 491 Simonson, J.M., see Dai, S. 494 Simopoulos, A. 328 Simopoulos, A., see Kallias, G. 328 Simopoulos, A., see Papavassiliou, G. 328 Simper, A., see Spencer, S. 493 Simpson, J.R., see Quijada, M. 296 Simpson, J.R., see Quijada, M.A. 269 Simsa, Z., see Jirák, Z. 291 Singh, D.J. 6 Singh, D.J., see Feldman, J.L. 11 Singh, D.J., see Nordstrom, L. 6, 12, 13 Singh, M., see Geraldes, C.F.G.C. 410 Singh, M., see Sherry, A.D. 411–413 Singh, R., see Sandhu, S. 497 Singh, R.K., see Kumar, D. 326 Singleton, J., see Kusters, R.M. 290

Sinitsyn, B.V., see Sobolev, B.P. 150, 202 Sinkov, S., see Billard, I. 470, 495, 501–503, 506 Sipe, J.P., see Horrocks Jr., W.deW. 367, 379 Sirvent, C., see Bauer, E.D. 8, 12, 15, 17, 24 Sisoeva, T.F., see Rezukhina, T.N. 209, 212 Skakovsky, E., see Rykov, S. 497 Skelton, B.W., see Harrowﬁeld, J.M. 405–407 Skierbiszewski, C., see Jantsch, W. 525, 580 Skierbiszewski, C., see Przybylinska, H. 525, 580 Skinner, H.B. 192, 234 Skolozdra, R., see Kaczmarska, K. 112, 113 Skolozdra, R.V. 41, 46, 52, 53, 59, 60, 67, 73, 80, 82, 84, 86–88, 112, 113, 117, 120–123, 132, 133 Skolozdra, R.V., see Aliev, F.G. 118 Skolozdra, R.V., see Kobzenko, G.F. 36 Skumryev, V. 312 Skylaris, C.-K., see Spencer, S. 493 Slack, G.A. 11, 29 Slack, G.A., see Nolas, G.S. 11 Slebarski, A. 45, 59, 60, 100, 113 Slebarski, A., see Bauer, E.D. 8, 12, 15, 17, 24 Slebarski, A., see Kaczmarska, K. 80, 112, 113 Slichter, C.P., see Sakaie, K.E. 296 Slov’ev, S.I., see Nisel’son, L.N. 236, 238 Slovyanskikh, V.K. 94, 95, 140 Slykhouse, T.E., see Fitch, R.A. 516 Smith, D.F., see Walden, G.E. 166–168, 179, 222 Smith, D.W. 280 Smith, F.C., see Parker, D. 420 Smith, R.I., see Pinsard-Gaudart, L. 268, 280 Smith, R.M., see Martell, A.E. 381 Smolyaninova, V., see Zhao, G. 326 Smolyaninova, V.N. 321, 327, 329 Smolyaninova, V.N., see Huang, Q. 328, 329 Snellgrove, T., see Denning, R. 557 Snider, W.E., see Hirayama, C. 196, 197, 239 Snow, N.H., see Sharman, K.S. 470 Snyder, G.J., see Watcharapasorn, A. 6, 7, 12, 13, 29 Snyder, S.W., see Metcalf, D.H. 489 Sobolev, B.P. 150, 200–203 Soderholm, L., see Xue, J.S. 12 Sofo, J.O. 6 Soga, N. 523, 555 Söhnel, O. 173 Soini, E. 509 Sologub, O. 41–43, 45–49, 51–54, 56–63, 65–69, 72–76, 79–93, 102, 103, 119–123, 133, 137 Sologub, O., see Flandorfer, H. 127 Sologub, O., see Protsyk, O. 45, 53 Sologub, O., see Salamakha, P. 56, 109

AUTHOR INDEX Sologub, O.L. 58, 72, 91, 106 Solomon, I. 356, 359, 361 Solomonik, V.G. 186 Solzi, M., see Allodi, G. 328, 337 Sommerer, S.O., see Cundari, T.R. 185, 189 Sommers, J.A. 151, 157, 158, 166–168 Song, C., see Fisher, I.R. 90, 91, 134, 135, 137 Sonier, J.E., see Heffner, R.H. 298, 325 Sonntag, R., see Krupicka, S. 338 Sood, A.K., see Joshi, J.P. 336 Spaeth, J.-M., see Tröster, Th. 523, 550 Spain, I.L., see Merkle, L.D. 522, 572–574 Specht, H., see Monsallier, J.M. 506 Spedding, F.H. 149, 162, 164, 165, 174, 176, 178, 200–213, 215, 216, 219 Spence, T.G., see Morss, L.R. 218 Spencer, S. 493 Spiliadis, S. 358, 377, 415 Spiliadis, S., see Pinkerton, A.A. 357, 365, 366 Spiridonov, V.P. 227 Spiridonov, V.P., see Giricheva, N.I. 229 Spirlet, M.-R. 420 Springer, C.S., see Ren, J. 433 Srijaranai, S., see Cunningham, J. 489, 497 Srivastava, S. 291, 292 Stang, P.J., see Leininger, S. 355 Stangret, J. 482 Stankiewicz, J. 292 Stankus, S.V. 150, 200–203 Stankus, S.V., see Khairulin, R.A. 178, 202 Stankus, S.V., see Lyapunov, K.M. 164, 165, 176 Stapor, A. 525, 578 Staub, U., see Mesot, J. 524, 535 Steed, J.W. 355 Steemers, F. 494 Steer, R.P., see Sikorski, M. 489 Stein, G., see Haas, Y. 471, 472, 475–477, 480 Steinberg, D.J., see Mao, H.K. 518 Steiner, W., see Leithe-Jasper, A. 26 Steiner, W., see Weitzer, F. 44, 59, 65, 73 Steinfeld, J. 487 Steinﬁnk, H., see Bodnar, R.E. 37 Steinﬁnk, H., see Wang, R. 48, 49, 75 Steinle, E., see Aas, W. 500 Steinle, E., see Fanghänel, T. 500 Stetskiv, A.O. 50, 55, 109, 111 Stetson, N.T. 15 Stevens, W.J. 148 Stevens, W.J., see Cundari, T.R. 148 Stewart, D.C., see Carnall, W.T. 494 Stock, M., see Yersin, H. 523, 569

629

Stoddart, J.F., see Balzani, V. 355 Stoll, H., see Dolg, M. 148, 183, 187–189 Stolyarova, V.L. 235 Storozhenko, T.P. 215–217 Storozhenko, T.P., see Khanaev, E.I. 214 Stout, E.W. 357, 371 Strasser, J., see Yersin, H. 523, 569, 570 Strohecker, L.A., see Cundari, T.R. 185, 189 Struck, C.W. 196, 239, 240, 567, 568, 572 Struck, C.W., see Fonger, W.H. 523, 524, 567 Struzhkin, V.V., see Goncharov, A.F. 522, 582 Stryla, Z., see Meinrath, G. 495, 497, 501 Stubbleﬁeld, C.T. 212, 215 Stubbleﬁeld, C.T., see Machlan, G.R. 214, 215, 221 Stucki, F., see Ott, H.R. 55 Stucky, G.D., see Suib, S.L. 481 Stump, N.A. 523, 557 Stump, N.A., see Chen, G. 523, 524, 557, 558 Stumpf, T. 495 Stuve, J.M. 213, 215, 216, 219–221 Stuve, J.M., see Montgomery, R.L. 219 Su, J., see Zhu, C. 326 Suaaidi, M., see García-Muñoz, J.L. 323 Subías, G. 323 Subramanian, P.R., see Massalski, T.B. 36 Sudnick, D.R., see Horrocks Jr., W.deW. 477–480, 484, 495, 497, 499, 501, 503, 504 Sugai, S., see Takenaka, K. 321 Suganuma, H., see Arisaka, M. 473, 474, 481 Sugawara, H. 8, 9, 18, 23 Sugawara, H., see Aoki, Y. 17–19 Sugawara, H., see Keller, L. 17, 23 Sugawara, H., see Matsuda, T.D. 17 Sugawara, H., see Sato, H. 6, 8, 12, 17, 18, 22, 23 Suib, S.L. 481 Suimetsu, T., see Salamakha, P. 56, 109 Sullivan, J.C., see Nash, K.L. 493 Sun, J.Z., see Xiao, G. 328 Supkowski, R.M. 481–483 Suvorov, A.V. 234 Suzuki, H. 58, 78 Suzuki, J., see Yamada, Y. 315 Suzuki, K., see Markovich, V. 325 Suzuki, T., see Kohgi, M. 521 Suzuki, T., see Naka, T. 521 Suzuki, T., see Okayama, Y. 521 Suzuki, T., see Oohara, Y. 521 Suzuki, T., see Yoshizawa, H. 521 Sviridov, L.A., see Morozkin, A.V. 40, 81, 83–85, 87–89, 93, 108

630

AUTHOR INDEX

Swiegers, G.F. 355, 393 Swingler, D.L., see Ciach, S. 236, 237 Syassen, K. 525, 550 Syassen, K., see Goncharov, A.F. 522, 582 Syassen, K., see Huber, G. 523, 530 Syassen, K., see Loa, I. 268 Syassen, K., see Stapor, A. 525, 578 Syassen, K., see Zimmer, H.G. 523 Szabo, G. 275 Szymczak, H., see Ilisavskii, Y. 326 Szymczak, H., see Troyanchuk, O.Ya. 275 Szytuła, A., see André, G. 123 Szytula, A., see Zigmunt, A. 61, 69, 74, 83, 85, 87 Tachi, K., see Shirotani, I. 7–9, 12 Tachiya, M. 489 Taguchi, A. 525, 578 Taguchi, A., see Hogg, R.A. 524, 555, 579 Taguchi, A., see Takarabe, K. 524, 525, 578–580 Tajima, K., see Shimomura, S. 326, 327 Tajiri, A., see Konami, H. 441–443 Takabatake, T., see Katoh, K. 118 Takabatake, T., see Salamakha, P. 56, 109 Takabatake, T., see Sologub, O.L. 91 Takagi, H., see Cava, R.J. 56 Takagi, H., see Katsufuji, T. 275 Takahashi, H., see Kohgi, M. 521 Takahashi, H., see Okayama, Y. 521 Takahashi, H., see Oohara, Y. 521 Takahashi, H., see Shirotani, I. 9, 10 Takahashi, H., see Yoshizawa, H. 521 Takahashi, K. 481 Takahashi, K., see Nojiri, H. 317 Takahashi, K.T., see Saitoh, E. 269 Takahei, K., see Hogg, R.A. 524, 555, 579 Takahei, K., see Taguchi, A. 525, 578 Takahei, K., see Takarabe, K. 524, 525, 578–580 Takalo, H., see Latva, M. 494, 495 Takarabe, K. 524, 525, 578–580 Takarabe, K., see Hogg, R.A. 524, 555 Takata, M., see Machida, A. 336 Takata, M., see Moritomo, Y. 277, 284, 285 Takazawa, H., see Lee, C.H. 20 Takeda, N. 8, 12, 15–17, 21, 23, 24 Takeda, N., see Kanai, K. 13 Takegahara, K., see Kasaya, M. 49, 57, 58, 62, 129, 130 Takeishi, H., see Kimura, T. 479, 481 Takemura, K., see Zimmer, H.G. 523 Takenaka, K. 321 Takeya, H., see Adroja, D.T. 60, 61, 118

Takikawa, T., see Matsuhira, K. 20 Taldenkov, A., see Yakubovskii, A. 309 Taldenkov, A.N., see Babushkina, N.A. 308, 309 Tanaka, F. 471, 472, 474, 484, 491, 492 Tanaka, H., see Liu, X.J. 299 Tanaka, M., see Murakami, Y. 263 Tanaka, M., see Nishimura, G. 524 Tanaka, T., see Miyano, K. 291 Tang, J., see Shirotani, I. 9, 10 Tang, X. 29, 30 Tanner, P.A. 557 Tanner, P.A., see Mak, C.S.K. 525, 581 Tao, J., see Zuo, J.M. 326 Tatevskii, V.M., see Akishin, P.A. 224 Tatsumi, T., see Kasuga, K. 440 Taube, H., see Lewis, W.B. 364 Taylor, A.J., see Lobad, A.I. 326 Tcheou, F., see Quezel, S. 275 Tchuiko, A.C., see Abdusalamova, M.N. 36, 37 Tedenac, J.C., see Ravot, D. 10, 11, 13 Teipen, R., see Uhlenbruch, S. 317 Tercier, N., see Blanzat, B. 523, 524, 574 Terreno, E., see Aime, S. 357, 360, 362, 433 Terreno, E., see Zhang, S. 355 Tetenbaum, M., see Flotow, H.E. 154 Thaller, A., see Laenen, R. 482 Thalmeier, P. 582 Thiel, G. 204 Thiel, G., see Seifert, H.J. 203, 205 Thiel, J., see Hornbostel, M.D. 8 Thistlethwaite, P.J., see Ciach, S. 236, 237 Thoma, R.E. 201–203, 206, 207 Thomas, J.M., see Reller, A. 282 Thompson, J.D., see Neumeier, J.J. 299 Thompson, J.D., see Yoshinari, Y. 328 Thompson, J.R., see Sales, B.C. 7, 9–11, 13, 29, 31 Thorn, R.J., see McCreary, J.R. 234, 235 Thornton, M.J. 124 Thouvenot, P. 507 Tichy, R.S. 277 Tiﬂova, L.A. 213, 216, 218, 220, 221 Tiﬂova, L.A., see Monaenkova, A.S. 218 Timmerman, P., see Prins, L.J. 393 Timofeev, S.S., see Abulkhaev, V.D. 94 Tippett, L., see Cundari, T.R. 185, 189 Tkachenko, N.L., see Sobolev, B.P. 150, 200–203 Többens, D.M., see Pissas, M. 329 Tobe, K. 266, 269 Tobe, K., see Saitoh, E. 269 Todo, S., see Shirotani, I. 7–9, 12, 21 Todo, S., see Uchiumi, T. 7–9, 12

AUTHOR INDEX Tokarczyk, B., see Mac, M. 491 Tokura, Y. 330, 341 Tokura, Y., see Arima, T. 279 Tokura, Y., see Asamitsu, A. 291, 319 Tokura, Y., see Causa, M.T. 326 Tokura, Y., see Chun, S.H. 298 Tokura, Y., see Dai, P. 325 Tokura, Y., see Fiebig, M. 291 Tokura, Y., see Fiebig, M.K. 291 Tokura, Y., see Granado, E. 329 Tokura, Y., see Kajimoto, R. 337 Tokura, Y., see Kawano, H. 336 Tokura, Y., see Kimura, T. 336 Tokura, Y., see Kiryukin, V. 291 Tokura, Y., see Kumagai, K. 311 Tokura, Y., see Kuwahara, H. 330, 331, 336, 337 Tokura, Y., see Martin, M.C. 322 Tokura, Y., see Miyano, K. 291 Tokura, Y., see Moritomo, Y. 291, 311 Tokura, Y., see Murakami, Y. 263 Tokura, Y., see Ogawa, K. 291 Tokura, Y., see Okuda, T. 325 Tokura, Y., see Saitoh, E. 269, 321 Tokura, Y., see Shimomura, S. 326, 327 Tokura, Y., see Tobe, K. 266, 269 Tokura, Y., see Tomioka, Y. 291, 294, 297 Tokura, Y., see Urushibara, A. 311 Tokura, Y., see Yoshizawa, H. 291 Tokura, Y., see Zhou, J.-S. 311 Tokura, Y., see Zimmermann, M.V. 264 Tolentino, H. 518 Tolmach, P.I. 157, 158, 160 Tolmach, P.I., see Gorbunov, V.E. 157, 158, 160 Tominaga, T., see Scully, A.D. 489 Tominaga, T., see Takahashi, K. 481 Tomioka, Y. 291, 294, 297 Tomioka, Y., see Asamitsu, A. 291, 319 Tomioka, Y., see Chun, S.H. 298 Tomioka, Y., see Dai, P. 325 Tomioka, Y., see Fäth, M. 298 Tomioka, Y., see Fiebig, M. 291 Tomioka, Y., see Fiebig, M.K. 291 Tomioka, Y., see Kawano, H. 336 Tomioka, Y., see Kimura, T. 336 Tomioka, Y., see Kiryukin, V. 291 Tomioka, Y., see Kumagai, K. 311 Tomioka, Y., see Kuwahara, H. 333, 337 Tomioka, Y., see Miyano, K. 291 Tomioka, Y., see Moritomo, Y. 291 Tomioka, Y., see Ogawa, K. 291 Tomioka, Y., see Okuda, T. 325

631

Tomioka, Y., see Tokura, Y. 330, 341 Tomioka, Y., see Yoshizawa, H. 291 Tomioka, Y., see Zimmermann, M.V. 264 Tomiyasu, H., see Park, Y.Y. 489, 491, 492, 498 Tomiyasu, H., see Yamamura, T. 491, 492 Tomiyasu, H., see Yayamura, T. 473 Tomka, G.J., see Thornton, M.J. 124 Tomuschat, C. 77, 78 Tondre, C., see Moulin, C. 501 Töpfer, J. 269, 286–289 Torikachvili, M.S. 6, 8, 17, 22 Torikachvili, M.S., see Meisner, G.P. 6, 12 Torrance, J.B., see Arima, T. 279 Torriani, I., see Granado, E. 284, 329 Toth, E. 363, 454 Toth, E., see Hedinger, R. 454 Tóth, É., see Sherry, A.D. 433 Totrova, G.A., see Gavrichev, K.S. 161, 163 Totrova, G.A., see Gorbunov, V.E. 157, 158, 160 Totrova, G.A., see Tolmach, P.I. 157, 158, 160 Tourillon, G., see Tolentino, H. 518 Tovar, M., see Causa, M.T. 326 Tovar, M., see Rivadulla, F. 321 Tran, C.D. 484 Tran, V.H., see Bauer, E. 24 Tran-Thi, T.H., see Mooney, W. 497 Traverso, O., see Allsopp, S.R. 473, 474 Tremel, W., see Mozharivskyj, Yu. 86, 138, 139 Trinquet, E., see Bazin, H. 509 Tritt, T.M., see Nolas, G.S. 3, 11, 27, 29, 30 Trlifaj, M. 573 Trommer, R. 578 Tröster, Th. 521–523, 527, 529, 531–533, 536, 541–543, 545, 546, 550, 551 Tröster, Th., see Bungenstock, C. 521, 529, 532–535, 537, 541–544, 546 Tröster, Th., see Burdick, G.W. 548 Tröster, Th., see Dierolf, V. 525, 529, 555 Tröster, Th., see Gregorian, T. 521, 522 Tröster, Th., see Jayasankar, C.K. 522, 547, 581 Tröster, Th., see Lavin, V. 522, 523 Tröster, Th., see Mak, C.S.K. 525, 581 Tröster, Th., see Shen, Y.R. 522 Troxler, L., see Berny, F. 358 Troyanchuk, O.Ya. 275 Trümbach, D., see Yersin, H. 523, 569, 570 Tsintsadze, G.A., see Lukin, S.N. 524, 536 Tsuruta, C., see Li, J.Q. 329 Tupolev, V.S., see Molodkin, A.K. 208 Tups, H., see Syassen, K. 525 Turano, P., see Bertini, I. 361

632

AUTHOR INDEX

Turley, W.D., see Gleason, J.K. 524, 551, 566, 568 Turro, C.J., see Fu, P.K.L. 355 Tutui, M., see Kasuga, K. 440 Tweedle, M.F., see Chang, C.A. 420 Tyagel’sky, P.V., see Khairulin, R.A. 202 Tyner, C.E. 523, 550 Uchiumi, T. 7–9, 12 Uchiumi, T., see Sekine, C. 7, 15, 19–21, 23, 25, 26 Uchiumi, T., see Shirotani, I. 7, 9, 13, 21 Uebach, W., see Seifert, H.J. 203, 204 Uehara, M. 323, 327–329, 340 Uehara, M., see Kim, K.H. 327, 328 Uehara, M., see Li, J.Q. 329 Uehara, M., see Podzorov, V. 327 Uemura, Y.J., see Heffner, R.H. 325 Ueno, K., see Lee, C.H. 20 Uggeri, F., see Aime, S. 420, 422, 433 Uher, C. 3, 27 Uher, C., see Chen, B. 13 Uher, C., see Meisner, G.P. 11 Uher, C., see Morelli, D.T. 11 Uhlenbruch, S. 317 Uhlenbruck, S., see Klingeler, R. 315 Ulivi, L., see Bungenstock, C. 521, 529, 533, 535 Ulrich, G. 358 Umemoto, K., see Fujita, M. 355 Uppal, M.K., see Reller, A. 282 Urland, W. 521, 545 Urland, W., see Gunselius, H. 151 Urosevic, V.V. 522 Urushibara, A. 311 Ushenin, S.N., see Lebedev, V.A. 36 Uspensky, E., see Gaft, M. 480 Vallet-Regí, M., see Alonso, J. 324 Valtancoli, B., see Bazzicalupi, C. 492, 509 Valtancoli, B., see Bianchi, A. 426 van Bekkum, H., see Corsi, D.M. 356 van de Burgt, L.J., see Wang, Z.M. 478, 494, 495, 499, 505 van den Brink, J. 269 Van der Tol, E., see Steemers, F. 494 Van Roosmalen, J.A.M. 267 van Rossum, B.J., see Mentink, S.A.M. 54 van Santen, J.H., see Jonker, G.H. 265 Van Tendeloo, G., see Gordon, I. 326 Van Valkenburg, A., see Weir, C.E. 516 van Veggel, F., see Klink, S.I. 471, 494–496

van Veggel, F.C.J.M., see An, Y. 405, 481, 483, 494 van Vlaanderen, P., see Cordfunke, E.H.P. 152, 207, 208 Vanacken, J., see Gordon, I. 326 VanOpdenbosch, N., see Kasuga, K. 440 Vasil’ev, V.V., see Laptev, D.M. 210–212, 216 Vasiliu-Doloc, L. 299, 318, 321 Vasiliu-Doloc, L., see Quijada, M.A. 269 Vassallo, P., see Brunetti, B. 195, 237, 239, 240 Vázquez-Vázquez, C., see Causa, M.T. 326 Vázquez-Vázquez, C., see Mira, J. 295 Veale, C.R., see Harris, A.L. 204 Védrine, A., see Labeau, M. 203 Vega, D., see Levy, P. 328 Veillet, P., see Anane, A. 291 Venkataraman, C., see Zimmermann, M.V. 264 Venkatesan, T., see Quijada, M. 296 Venkatesan, T., see Saraf, L.V. 309 Venkatesan, T., see Zhao, G.-M. 308 Venkatesan, T., see Zhao, Y.G. 296, 328 Venteicher, R.F., see Wong, C.P. 449 Verboom, W., see Steemers, F. 494 Vergés, J.A., see Mayr, M. 326 Verhoeven, J., see Steemers, F. 494 Verhoeven, J.W., see Werts, M.H.V. 481 Vettier, C. 518, 521, 535 Vettier, C., see Mesot, J. 524, 535 Vial, J.-C., see Oppenländer, A. 522 Viallesoubranne, C., see Billard, I. 470, 495, 501–503, 506 Vigliante, A., see Kiryukin, V. 291 Vijaya Lakshmi, K. 121, 124 Vila, A.J., see Bertini, I. 361 Villani, A.R. 195, 236, 238–240 Villani, A.R., see Brunetti, B. 195, 236, 238, 239 Villani, A.R., see Piacente, V. 195, 237, 239, 240 Villars, P. 37 Vinokurova, N.G., see Goryushkin, V.F. 182, 209 Vinokurova, N.G., see Poshevneva, A.I. 182, 208 Viret, M., see Anane, A. 291 Virtuani, M., see Bianchi, A. 426 Viswanathan, K.S., see Peter, S. 507 Vlasenko, L.S., see Huhtinen, H. 326 Vlasenko, M.P., see Huhtinen, H. 326 Vogel, G. 203–205 Vogel, R. 36 Vogl, P., see Trommer, R. 578 Vogt, J., see Zakharov, A.V. 184, 186, 190, 191, 195, 229, 232

AUTHOR INDEX Vogt, N., see Zakharov, A.V. 184, 186, 190, 191, 195, 229, 232 Vogt, O., see Burlet, P. 55 Vogt, O., see Frick, B. 94, 140 Vogt, O., see Rossat-Mignod, J. 55, 57 Vohra, Y.K., see Hua, H. 521, 522, 552, 553 Vohra, Y.K., see Liu, J. 523, 553 Vold, R.L. 364 Voloshin, V.A. 521–524, 531, 559, 571, 581 Voltz, R. 483 von Helmolt, R. 290 von Molnár, S., see Hudspeth, H.D. 326 von Molnár, S., see Raquet, B. 326 Vorontsov, E.S., see Laptev, D.M. 203, 204 Vottéro, P.J.A., see Chapon, D. 454, 455 Vratislav, S., see Jirák, Z. 275, 291 Vuilleumier, J.J., see Marcantonatos, M.D. 497 Vybornov, M., see Sologub, O. 43, 46, 47, 51, 54, 60, 68, 74, 103 Wachter, P., see Neuenschwander, J. 522, 523, 525 Wada, M., see Sato, S. 572 Wadsö, I., see Fitzgibbon, G.C. 210 Wagman, D.D., see Cox, J.D. 173 Wagman, D.D., see Parker, V.B. 173 Wagner, P., see Gordon, I. 326 Wai, C.M., see Addleman, R.S. 489, 509 Wakabayashi, N., see Dai, P. 325 Wakabayashi, N., see Shimomura, S. 326, 327 Wakabayashi, Y., see Zimmermann, M.V. 264 Walden, G.E. 166–168, 179, 222 Waldfried, C., see McIlroy, D.N. 295 Walker, P.J., see Garton, G. 205 Walters, M.K., see Hutchinson, F. 179 Wamsley, P.R. 525, 575, 577 Wamsley, P.R., see Lochhead, M.J. 471 Wang, L. 523, 524, 551, 568 Wang, L., see Chi, Y. 523, 524, 530, 533, 534, 536, 539 Wang, L., see Liu, S. 523, 524, 529, 530, 533, 539 Wang, L., see Wang, Q. 524, 530, 538 Wang, M.E., see Chan, J.Y. 134 Wang, P.J. 522–525, 550 Wang, Q. 523, 524, 530, 533, 534, 538 Wang, Q., see Chi, Y. 523, 530, 533, 534, 539 Wang, R. 48, 49, 75 Wang, S., see Chen, G. 522, 549, 550 Wang, X.Z., see Culp, T.D. 525, 580 Wang, Y. 478, 494 Wang, Y.S., see Alexandrov, A.S. 308 Wang, Z., see Choppin, G.R. 495

Wang, Z.M. 478, 494, 495, 499, 505 Wang, Z.M., see De Sa, G.F. 471, 483 Wasse, J.C. 179 Wasse, J.C., see Hutchinson, F. 179 Wasylishen, R.E. 363 Watcharapasorn, A. 6, 7, 12, 13, 29 Watkins, S.F., see Fronczek, F. 381 Watson, R.E., see Freeman, A.J. 377 Waugh, J.S., see Vold, R.L. 364 Weaver, H.T., see Schirber, J.E. 521 Webb, D., see Chan, J.Y. 134 Webb, D.J., see Chan, J.Y. 90 Webb, S., see Hemmilä, I. 509 Webber, S.E., see Morrison, M.E. 489 Weber, J., see Ouali, N. 379, 390, 405–410 Weber, J., see Stapor, A. 525, 578 Webster, G.A. 524, 551, 567, 568, 574 Wecker, J., see von Helmolt, R. 290 Weger, H., see Fanghänel, T. 500 Weger, H.T., see Fanghänel, T. 500 Wei, W., see Ogawa, K. 291 Weill, G., see Gonzalez, J. 518 Weir, C.E. 516 Weiss, R., see Buchler, J.W. 449, 450 Weiss, R., see Moussavi, M. 440 Weitzer, F. 44, 59, 65, 73 Wells Jr., J.C. 186, 227, 229, 230 Wenski, G. 62, 71, 78, 107 Werts, M.H.V. 481 Werts, M.H.V., see Klink, S.I. 471, 494–496 Wertz, J.E. 359, 364 Wesley, R.D. 186, 191, 224, 225 Wessels, B.W., see Culp, T.D. 525, 580 Westrum Jr., E.F. 154, 157 Westrum Jr., E.F., see Deline, T.A. 161, 163 Westrum Jr., E.F., see Sommers, J.A. 151, 157, 158, 166–168 White, A.H., see Harrowﬁeld, J.M. 405–407 White, W.T., see Xue, J.S. 12 Wicholas, M., see Buchler, J.W. 450–453 Wickersheim, K.A. 567 Wickleder, M.S., see Meyer, G. 149 Wiebe, C.R. 282 Wiesinger, G., see Weitzer, F. 44, 59, 65, 73 Wiesinger, W., see Leithe-Jasper, A. 26 Wietzke, R., see Bretonnière, Y. 393 Wilcott, M.R. 373, 385 Wilkinson, M.K., see Koehler, W.C. 259 Willets, A., see Spencer, S. 493 Williams, A.F., see Piguet, C. 384, 385 Williams, C., see Beitz, J.V. 495, 497, 501

633

634

AUTHOR INDEX

Williams, J., see Beeby, A. 481–484 Williams, J., see Parker, D. 484, 493, 494 Williams, J.A.G., see Dickins, R.S. 482 Williams, J.A.G., see Parker, D. 491, 509 Williams, R.J.P., see Alsaadi, B.M. 361, 405–407 Williams, R.J.P., see Barry, C.D. 363 Williams, R.J.P., see Bleaney, B. 357, 365, 371 Williams, R.K., see Sales, B.C. 2, 7, 9, 11, 13, 26, 29 Willig, F., see Eichhorn, M. 569 Wilmarth, W.R. 521, 522, 558 Wilmarth, W.R., see Daniel, J.F. 151, 205 Wilmarth, W.R., see Young, J.P. 558 Wilson, K.G. 13 Wilson, L.J., see Chang, C.A. 420 Wilson, M., see Hutchinson, F. 179 Wimmer, H. 500 Wimmer, H., see Kim, J.I. 496 Wimmer, H., see Panak, P. 494, 495 Windsor, M.W., see Kropp, J.L. 475–477, 480 Winkler, E., see Rivadulla, F. 328, 330–335, 337–342 Wintgens, V., see Pouliquen, J. 488 Winzen, H., see Syassen, K. 525, 550 Wipff, G., see Berny, F. 358 Wipff, G., see Fraternali, F. 358 Wipff, G., see Ulrich, G. 358 Wirth, S., see Raquet, B. 326 Wohlford, D.J., see Ren, S.Y. 580 Wojakowski, A., see Charvillat, J.-P. 57, 61, 71, 75, 81 Wold, A. 289 Wold, A., see Goodenough, J.B. 265, 267, 269, 270 Wolford, D.J. 555 Woll, P., see Cordier, G. 43, 44, 46 Woll, P., see Sologub, O. 43, 46, 47, 51, 54, 60, 68, 74, 103 Wollan, E.O. 262, 327 Wollan, E.O., see Koehler, W.C. 259 Wollesen, P. 43, 44, 46, 48, 49, 51, 52, 54, 57–61, 63, 66, 68, 70, 72, 73, 75, 80, 83 Wong, C.P. 449 Wood, V.E. 275 Woods, M., see Aime, S. 426, 429 Woods, M., see Beeby, A. 481–484 Woodward, F.M., see Maple, M.B. 22 Woodwark, D., see Denning, R. 557 Worledge, W.C. 323 Wortmann, G., see Bungenstock, C. 540 Wortmann, G., see Lübbers, R. 518

Wright, A.O. 523, 524 Wright, A.O., see Olsen, L.R. 523 Wright, J.C., see Olsen, L.R. 523 Wright, J.C., see Wright, A.O. 523, 524 Wu, S. 469, 499 Wu, S.L. 492 Wu, T., see Zhao, Y.G. 328 Wybourne, B.G. 526, 566 Xavier, A.V., see Barry, C.D. 363 Xavier, A.V., see Bleaney, B. 357, 365, 371 Xia, S., see Mak, C.S.K. 525, 581 Xia, Z.J., see Bertini, I. 357, 361 Xiao, G. 328 Xie, J.Q., see Zheng, R.K. 328 Xiong, P., see Hudspeth, H.D. 326 Xiong, P., see Raquet, B. 326 Xiong, X. 311 Xiong, X., see Dabrowski, B. 311 Xu, W., see Bare, W.D. 470, 509 Xue, J.S. 12 Xue, Z.L., see Dai, S. 494 Yagi, T., see Sekine, C. 7, 15, 19–21, 25, 26 Yagi, T., see Shirotani, I. 7–10, 12, 21 Yagi, T., see Uchiumi, T. 7–9, 12 Yagi, T., see Yusa, H. 523, 553 Yakabovsky, A., see Shames, A.I. 338 Yakhkind, E., see Ilisavskii, Y. 326 Yakovlev, E.N., see Kasatochkin, S.V. 524 Yakubovskii, A. 309 Yakubovskii, A., see Kumagai, K. 311 Yamada, Y. 315 Yamada, Y., see Lee, K.P. 492 Yamaguchi, T., see Suzuki, H. 58, 78 Yamamoto, A., see Lee, C.H. 20 Yamamoto, E., see Matsuda, T.D. 17 Yamamoto, H., see Soga, N. 523, 555 Yamamoto, K., see Saitoh, E. 269 Yamamoto, N., see Katsufuji, T. 275 Yamamoto, N., see Machida, A. 336 Yamamura, T. 491, 492 Yamashita, S., see Tanaka, F. 471, 472, 474 Yanase, N., see Sekine, C. 13 Yang, J., see Meisner, G.P. 11 Yang, K.N., see Meisner, G.P. 6, 12 Yano, H., see Kim, Y.C. 219 Yashvili, T.S. 215 Yashvili, T.S., see Gvelesiani, G.G. 210, 214 Yates, E.C., see Wickersheim, K.A. 567 Yayamura, T. 473

AUTHOR INDEX Yelon, W.B., see Mehta, A. 69 Yersin, H. 523, 569, 570 Yersin, H., see Eichhorn, M. 569 Yin, H.Q., see Zhou, J.-S. 269, 271, 272, 284 Yokoya, T., see Kanai, K. 13 Yokoyama, H., see Kanno, H. 482 Yokoyama, M., see Sekine, C. 20 Yokoyama, Y. 491, 497 Yokoyama, Y., see Moriyasu, M. 489, 491, 504 Yoo, C.S. 522, 549, 550 Yoon, S. 326 Yoon, S., see Naler, S. 328 Yoshida, Z., see Arisaka, M. 473, 474, 481 Yoshida, Z., see Kimura, T. 471–473, 479 Yoshida, Z., see Lis, S. 489, 491 Yoshida, Z., see Nagaishi, R. 497 Yoshimoto, M., see Soga, N. 523, 555 Yoshinari, Y. 328 Yoshizawa, H. 291, 521 Yoshizawa, H., see Kajimoto, R. 337 Yoshizawa, H., see Kawano, H. 336 Yoshizawa, H., see Kohgi, M. 521 Yoshizawa, H., see Okayama, Y. 521 Yoshizawa, H., see Oohara, Y. 521 Yoshizawa, M., see Fujita, M. 355 Yoshizawa, Y., see Kawano, H. 311 Yotsuyanagi, T., see Katsumura, Y. 489, 496, 497, 508 Young, J.P. 558 Young, J.P., see Haire, R.G. 558 Young, J.P., see Peterson, J.R. 522, 558 Young, J.P., see Wilmarth, W.R. 521, 522, 558 Young, M., see Rakicioglu, Y. 508 Yu, J., see Jung, J.H. 323 Yudin, V.M. 276 Yuhasz, W.M., see Maple, M.B. 22 Yunoki, S., see Dagotto, E. 261 Yusa, H. 523, 553 Yuzhelevski, Y. 326 Zaanen, J. 256, 277 Zaitsev, S.A., see Loktyushina, N.S. 186, 228, 229 Zakharov, A.V. 184, 186, 190, 191, 195, 229, 232 Zakharov, A.V., see Girichev, G.V. 229 Zakharov, A.V., see Giricheva, N.I. 184, 186, 227 Zakharova, G.V., see Billing, R. 489, 491 Zakhvalinskii, V.S., see Huhtinen, H. 326 Zalyalyutdinov, M.K., see Aliev, F.G. 118 Zalymova, S.A., see Goryushkin, V.F. 180, 205, 206, 223 Zanicchi, G., see Riani, P. 41, 85, 87, 88, 91, 93

635

Zapf, V.S., see Bauer, E.D. 8, 12, 15, 17, 21, 22 Zapf, V.S., see Maple, M.B. 22 Zaplatynsky, O.V. 67, 69, 71 Zasorin, E.Z. 184, 185, 224–231 Zasorin, E.Z., see Giricheva, N.I. 229 Zavalii, I.Yu. 40, 44, 138, 139 Zavalii, I.Yu., see Pecharsky, V.K. 45, 98 Zekovic, Lj.D., see Jovani´c, B.R. 522, 524, 563 Zekovic, Lj.D., see Urosevic, V.V. 522 Zener, C. 257, 258 Zeng, L. 48 Zeng, Z., see Wiebe, C.R. 282 Zenkevich, L.V., see Evseeva, G.V. 236 Zerger, R.P., see Suib, S.L. 481 Zevtsova, Z.R., see Pashinkin, A.S. 237 Zhang, D., see Wang, Q. 524, 530, 538 Zhang, G., see Fisher, R.A. 326 Zhang, G., see Gordon, J.E. 326 Zhang, H., see Chi, Y. 524, 536 Zhang, J., see Lam, R. 55, 78 Zhang, J., see McIlroy, D.N. 295 Zhang, J.S. 65, 73 Zhang, L.W., see Zhao, Y.G. 328 Zhang, S. 355 Zhang, S., see Geraldes, C.F.G.C. 358, 378, 404, 405, 411, 414, 415, 417, 418, 420, 424, 425, 427, 429–432, 435–438, 442, 443, 451, 453 Zhang, S., see Ren, J. 420, 423–426, 429, 431, 433–435, 437–440 Zhang, S.G., see Jia, Y.Q. 184 Zhang, W., see Tran, C.D. 484 Zhang, X., see Smolyaninova, V.N. 327 Zhang, X.H., see Ren, Y.H. 326 Zhang, X.P., see Zhao, Y.G. 328 Zhang, X.Y., see Rozenberg, M.J. 261, 315 Zhang, Z., see Wang, L. 523, 524, 551, 568 Zhao, G. 326, 329 Zhao, G., see Smolyaninova, V.N. 327 Zhao, G.-M. 305, 307, 308 Zhao, G.-M., see Alexandrov, A.S. 308 Zhao, J., see Zhao, Y.G. 328 Zhao, Q., see Forsberg, J.H. 357, 358, 374, 380, 427–431, 439, 440 Zhao, X., see Chi, Y. 523, 533, 539 Zhao, X., see Liu, S. 523, 530, 533 Zhao, Y.G. 296, 328 Zhao, Z.X., see Li, J.Q. 329 Zheng, R., see Zhu, C. 326 Zheng, R.K. 328 Zhigarnovskii, B.M. 201, 203 Zhigarnovskii, B.M., see Gogadze, N.G. 201–203

636

AUTHOR INDEX

Zhou, J.-S. 264, 265, 268, 269, 271, 272, 276–282, 284, 300–302, 305–308, 311, 312, 316, 317, 319–322 Zhou, J.-S., see Archibald, W. 294, 295, 300 Zhou, J.-S., see Goodenough, J.B. 261, 272–274, 296, 298 Zhou, J.-S., see Liu, G.-L. 311, 313, 316, 318 Zhou, J.-S., see Overend, N. 303 Zhou, J.-S., see Rivadulla, F. 328, 330–335, 337–342 Zhu, C. 326 Zhu, C.F., see Zheng, R.K. 328 Zhu, M.H., see Zhao, Y.G. 328 Ziese, M., see Gordon, I. 326 Ziessel, R., see Ulrich, G. 358

Zimmer, H.G. 523 Zimmer, H.G., see Syassen, K. 525 Zimmermann, M.V. 264 Zimmermann, M.V., see Casa, D. 315 Zitserman, V.Y., see Berezhkovskii, A.M. 489 Zmbov, K.F. 234, 235 Zmbov, K.F., see Besenbuch, G. 235 Zmbov, K.F., see Kent, R.A. 234 Zou, G., see Chi, Y. 523, 530, 539 Zou, G., see Liu, S. 523, 524, 529, 530, 533, 539 Zuo, J.M. 326 Zvyagin, S. 338 Zygmunt, A. 61, 69, 74, 83, 85, 87 Zygmunt, A., see Slebarski, A. 45, 59, 60, 100, 113

SUBJECT INDEX antiferromagnetic t3 –O–t3 interactions 275, 285 antiferromagnetic t3 –O–t3 superexchange interactions 262, 276 antiferromagnetic to ferromagnetic transition 294 antisymmetric exchange 258, 264 atomic displacement parameter (ADP) 4, 11, 23 atomic orbitals 253 axial system 376, 377, 380 azacryptand 401

1,3,5-triamino-1,3,5-tridesoxy-cis-inositol 454 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetrakis (methylenephosphonic acid) 430 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetrakis (N ,N -diethylacetamide) 426 1,4,7,10-tetraazacyclododecane-N ,N ’,N ”,N ”’tetraacetic acid 419 1,4,7-triazacyclononane-N ,N ’,N ”-triacetic acid 410 2,6-bis{{1-ethyl-2-[6-(N ,N ’-diethylcarbamoyl)pyridin-2-yl]benzimidazol-5-methylene}(2-ethyl-benzimidazol-5-yl)}pyridine 455 2,6-bis(benzimidazole)pyridine 384 2,6-pyridinedicarboxylic acid 404 2,6-pyridinedicarboxylic acid-bis-diethylamide 387 2-{6-[N ,N -diethylcarboxamido]-pyridin-2-yl}1,1’-dimethyl-5,5’-methylene-2’-(5-methylpyridin-2-yl)bis(1H-benzimidazole) 393 2D orbital order–disorder transition 312

B2 O3 –Na2 O–Eu2 O3 (glass) 523 Ba2 SiO4 :Eu2+ 523 Ba5 Al2 Sb6 structure type 111 BaAl4 structure type 98 BaAl4 type related structures 141 BaBr2 523 bad metal 266, 287, 288, 302 BaF2 :Sm2+ 522 BaFCl:Sm2+ 522 BaFe4 Sb12 15 band structure 8 BaOs4 Sb12 15 BaRu4 Sb12 15 bending angle φ 251, 256, 275, 292, 306 bending of the (180◦ − φ) Mn–O–Mn bond angle 323, 342 bimetallic lanthanide complexes 443 binary systems R–Sb 36 bis{1-ethyl-2-[6’-carboxy)pyridin2’-yl]benzimidazol-5-yl}methane) 444 Bleaney’s factors 371 Bloch’s rule 279 bond length 183 – LnBr3 183 – LnCl3 183 – LnF3 183 – LnI3 183 bond-bending angle 261, 292, 304 bond-length ﬂuctuations 261, 262, 282, 284, 304, 321, 333, 341, 343 Born–Haber cycle 171, 172 Born–Landé equation 170 bulk paramagnetic susceptibility 356

A-type antiferromagnetic order 285 ab initio calculations of intrinsic parameters 545 absorption – of Cm(III) 494 – of lanthanides 469, 494 – of U(VI) 494 absorption lines under pressure 527 ADP 30 AF-FM insulator-conductor transition 340 agreement factor 373, 374, 385 AlB2 structure type 106, 139 angular overlap model 545 antiferromagnetic ﬂuctuations 336 antiferromagnetic order 20, 23, 25 antiferromagnetic order: type-CE 338, 339 antiferromagnetic phase converts abruptly to the conductive, ferromagnetic phase 305 antiferromagnetic state can be driven irreversibly to a ferromagnetic conductive state 292 antiferromagnetic superexchange interaction 256, 276, 343 637

638

SUBJECT INDEX

C-type antiferromagnetic order 284 C-type antiferromagnetic phase 283 Ca1−x Lax MnO3 , 0 x 0.2 283 Ca14 AlSb11 structure type 111, 138 Ca2 P2 O7 :Eu2+ 523 CaAl2 O4 :Eu2+ 523 CaAl2 Si2 structure type 98, 138 CaBe2 Ge2 structure type 99, 139 CaBPO5 :Eu2+ 523 CaCrO3 282 CaF2 :Ce3+ 521 CaF2 :Dy2+ 524 CaF2 :Er3+ 524 CaF2 :Eu3+ 523 CaF2 :Gd3+ 524 CaF2 :Pr3+ 521 CaF2 :Sm2+ 522 CaF2 :Tb3+ 524 CaF2 :Tm2+ 525 CaFCl:Sm2+ 522 CaFe4 Sb12 15 CaIn2 structure type 106, 139 CaMnO2.94 282 CaMnO3 256, 276, 277, 281, 282 canted-spin 318 canted-spin antiferromagnet 273, 340 canted-spin antiferromagnetic insulator 273 canted-spin antiferromagnetic phase 311 canted-spin ferromagnetic 292 canted-spin ferromagnetism 258 canted-spin, type-A antiferromagnetic order 269 Ca(PO3 )2 :Eu3+ (glass) 523 carrier concentration 13 carrier mass 17 CaTiO3 4 cation–anion resonance (electron-energy transfer) integral 277 CdF2 :Eu2+ 523 CdF2 :Gd3+ 524 CDWs 315, 317 CE AFI phase 328, 329, 332, 334, 335, 341 CE domains 329 CE phase 326–328 Ce–Ag–Sb 56 Ce–As–Sb 55 Ce–Au–Sb 58 Ce–Cd–Sb 57 Ce–Co–Sb 52 Ce–Cr–Sb 50 Ce–Cu–Sb 53 Ce–Cu–Sb, isothermal section 53, 54

Ce–Fe–Sb 51 Ce–Ga–Sb 54 Ce–Ge–Sb 55 Ce–Ge–Sb, isothermal section Ce–Hf–Sb 57 Ce–In–Sb 57 Ce–Li–Sb 49 Ce–M–Sb systems 49 Ce–Mn–Sb 50 Ce–Mn–Sb, isothermal section Ce–Ni–Sb 52 Ce–Ni–Sb, isothermal section Ce–Os–Sb 57 Ce–Pd–Sb 56 Ce–Pt–Sb 57 Ce–Rh–Sb 56 Ce–Ru–Sb 56 Ce–Sb 36 Ce–Se–Sb 55 Ce–Si–Sb 50 Ce–Si–Sb, isothermal section Ce–Sn–Sb 57 Ce–Te–Sb 57 Ce–Ti–Sb 50 Ce–V–Sb 50 Ce–Zn–Sb 54 Ce–Zr, Nb–Sb 55 Ce0.33 U0.67 Sb2 94 Ce0.6 La0.4 CuSb2 122 Ce0.8 La0.2 CuSb2 122 Ce1−x Lax RhSb 95 Ce12 Ga4 Sb23 54 Ce29 Mn13 Sb58 51 Ce2 Fe4 Sb5 52 Ce2 GeSb3 55, 109 Ce2 Pd9 Sb3 56 Ce2 Pd9 Sb3 structure type 95 Ce2 Sb 38 Ce2 Se3 –Sb2 Se3 section 55 Ce2 Si3 Sb5 50 Ce3 Au3−x Ptx Sb4 132, 133 Ce3 Au3 Sb4 58, 106, 129 Ce3 Cu3 Sb4 53, 132, 133 Ce3 GeSb 55, 111 Ce3 HfSb5 57 Ce3 NbSb5 55 Ce3 Pd6 Sb5 56, 113, 141 Ce3 Pd6 Sb5 structure type 97 Ce3 Pt3 Sb4 57, 129 Ce3 Rh3 Sb4 56, 133 Ce3 SiSb 50

55

50, 51 52, 53

50

SUBJECT INDEX Ce3 TiSb5 50 Ce3 ZrSb5 55 Ce4 Sb3 38 Ce5 Ge3 Sb2 55 Ce5 Sb3 38 Ce6 CuSb15 54 Ce6 Ge5−x Sb11+x 55, 135 Ce6 Mn0.4 Sb15 103 Ce6 MnSb15 51, 133, 134 Ce6 ZnSb15 54, 133, 134 Ce8 Pd24 Sb 56 Ce8 Pd24 Sb structure type 100 (Cex Sb1−x )2 Se3 55 CeAg2 Sb2 113 CeAgSb2 56, 102, 123, 124, 128 CeAs 521 CeAsx Sb1−x 55 CeAuSb 58 CeAuSb2 58, 121 Ce(C2 H5 SO4 )3 ·9H2 O 521 CeCdSb2 57 CeCo1−x Sb2 52 CeCrSb3 50, 72 CeCu1−x Sb2 53 CeCu2 Sb2 113 CeCu6 Sb3 53 CeCuSb2 53, 120–122 CEF 23 CeF3 :Pr3+ 521 CeFe0.6 Sb2 127 CeFe1−x Sb2 51 CeFe4 As12 13, 14 CeFe4 P12 12, 14 CeFe4 Sb12 10, 11, 13, 14, 16, 52 CeGa2 Al2 structure type 99, 139, 140 CeIn0.8 Sb2 57 CeLi2 Sb2 50 CeMn0.85 Sb2 51, 120 CeNi2+x Sb2−x 53, 141 CeNi2+x Sb2−x structure type 100 CeNi2.36 Sb1.64 100 CeNi2 Sb2 53, 112 CeNiSb 52, 116, 117 CeNiSb2 52, 121, 122 central-ﬁeld covalency model CFC 530, 533 CeOs4 As12 14 CeOs4 P12 13, 14 CeOs4 Sb12 14, 17, 57 CeP 521 CePd2 Sb2 56 CePdSb 56, 118

639

CePdSb2 56, 121 CePdSb3 56 CePtSb 57 CeRh2 Sb2 56 CeRhSb 56, 95, 109, 118 CeRu4 As12 13, 14 CeRu4 P12 12, 14 CeRu4 Sb12 14–16, 56 CeSb 38 CeSb (HP) 38 CeSb2 37, 38 CeSb2 (HT) 38 CeSbTe 57 CeScSi structure type 108, 137 CeSe30 Sb19 55 CeSnx Sb2 57 CeTex Sb1−x 57 CeVSb3 50 CeVSb3 , structure type 137 CeZn0.8 Sb2 54 CeZn1−x Sb2 54, 120 CeZnSb2 119 characteristic temperature 15, 26 charge and orbital ordering 286, 327, 328, 330, 343 charge and orbitally ordered 315 charge disproportionation 267 charge order 332 charge ordering 292, 315, 327, 329, 332, 335, 343 charge transfer state 551, 574 charge transfer states under pressure 549, 551, 567, 568 – La2 O2 S:Eu3+ 568 – R2 O2 S:Eu3+ 551, 567 charge-density wave 282, 284, 315, 323, 330, 332, 335, 343 charge-density/spin-density wave 261 charge-order ﬂuctuations 343 charge-ordered 327–329 charge-ordered phase 309 chelates – Eu3+ 523 – Gd3+ 524 – Sm3+ 522 – Tb3+ 524 chloride complexes 500 – of Cm(III) 474 – of lanthanides 473, 474 cluster glass 288, 290, 310, 311 Cm(III) – lifetime 473, 481

640

SUBJECT INDEX

CMR phenomenon 290, 317, 321, 324, 325 CO 332 CO phase 329, 332, 333, 335, 342 CO transition 333 CoAs3 2 colossal magnetoresistance 262 conductivity 27 conﬁguration interactions 536, 548, 550, 551, 561 – LaCl3 :Pr3+ 551 – LaOCl:Pr3+ 551 – LiYF4 :Pr3+ 551 – MFCl:Sm2+ 548 conﬁguration interactions under pressure 551 contact contribution 364 contact shifts 364 cooperative Jahn–Teller distortion 268, 273 cooperative Jahn–Teller Mn(III)-site distortions 285 cooperative oxygen displacements 255, 304 cooperative rotations 251, 263, 264, 275 coordination number 493 COP 28 correlation crystal ﬁelds under pressure LaCl3 :Nd3+ 547 correlation intrinsic parameter 548 correlation of luminescence properties with structural changes 557 correlation time 359 CoSb3 5 covalent mixing 260 covalent-mixing parameters 254 critical ﬁeld 22 cross-relaxation 573 crossover 334 crossover from localized to itinerant electron behavior 304 crossover from localized to itinerant electronic behavior 250, 261, 290, 293, 299, 311, 332, 343 crossover from localized to vibronic behavior 288 crossover from localized-electron to band magnetism 282 crossover from polaronic to itinerant electron behavior 304 crystal-ﬁeld 13, 21, 366, 368, 371, 372, 377, 380, 459 crystal-ﬁeld energies 158 crystal-ﬁeld energy – LnCl3 160 – LnF3 154 crystal-ﬁeld independent methods 377

crystal-ﬁeld parameters 368 crystal-ﬁeld parameters under pressure 535, 538, 539 crystal-ﬁeld splitting 157 crystal-ﬁeld splittings under pressure 535 crystal-ﬁeld strength under pressure 535, 538–540 – GdOBr:Eu3+ 539 – GdOCl:Eu3+ 539 – La2 O2 S:Eu3+ 538 – LaOBr:Eu3+ 539 – LaOCl:Pr3+ 539 – Na5 Eu(MoO4 )4 539 – ROCl:Pr3+ 539 – Y2 O2 S:Eu3+ 538 – YAG:Tb3+ 538 crystalline electric ﬁeld 17, 18, 20, 22 Cs2 NaTmCl6 525 CsCaF3 :Gd3+ 524 CsSmI3 522 cubic-ﬁeld splitting 254 Curie–Weiss behavior 332 Curie–Weiss paramagnetism 264, 336 Curie-spin relaxation 362 cyclotron effective mass 18 δ-function model 547, 548, 551 – LaCl3 :Nd3+ 548 – LaCl3 :Pr3+ 548 de Gennes double exchange 285, 292, 293, 310, 317, 333, 343 De Haas–van Alphen 18, 23 Debye temperature 9 diamagnetic shift 357 diamond anvil cell 517, 519 dicalcium protein calbindin D9k 374 dielectric screening model 530, 532 dimensionless ﬁgure of merit 27 direct exchange 256 disordered orbitals 272 displacive-type phase transition 23 disproportionation 255, 343 disproportionation reaction 266, 267, 273, 323 distance dependence of intrinsic parameters 547 distinguishable ferromagnetic phases 317 dithiomethylphosphinic acid 415 dithiophosphorus acid 415 divalent europium 479, 482, 483, 494 DOTA 419 DOTAM 426 DOTEA 426 DOTP 430 DOTTA 426

SUBJECT INDEX double-decker sandwich compound 449 double-exchange 257, 266, 267, 293, 307, 308, 332 DTMA 426 Dy–Ag–Sb 85 Dy–Au–Sb 85 Dy–Cr–Sb 84 Dy–Cu–Sb 84 Dy–Ge–Sb 84 Dy–M–Sb systems 84 Dy–Ni–Sb 84 Dy–Pd–Sb 85 Dy–Pt–Sb 85 Dy–Sb 37 Dy–Te–Sb 85 Dy–Zr–Sb 84 Dy0.33 U0.67 Sb2 94 Dy1.5 U1.5 Sb7 94 Dy2 Sb5 37, 39 Dy3 Au3 Sb4 85 Dy3 Cu3 Sb4 84, 133 Dy4 Sb3 (α) 39 Dy5 Ni2 Sb 84, 111 Dy5 Pd2 Sb 85 Dy5 Pt2 Sb 85 Dy5 Sb3 39 Dy6 Ge5−x Sb11+x 84, 135 DyAgSb2 85, 128 DyCrSb3 84 DyCuSb2 84, 121 dynamic phase segregation 282 DyNi2−x Sb2 84 DyNiSb 84, 116 DyNiSb2 84, 121 DyPd2 Sb 85 DyPdSb 85 DyPtSb 85 (DySb)1−x Nix 84 DySb2 (HT) 39 DySb(α) 39 DyTe3 Sb 85 DyZrSb 84 Dzialoshinskii vector 258, 264, 285, 311 eg 5 effective axial symmetry 368, 455 effective electronic magnetic momenta effective masses 28 effective nuclear charge 529, 534 Einstein frequency 11 elastic constant 11

356

electric quadrupole 22 electron coupling to oxygen vibrations 305 electron–crystal 30 electron–electron coulomb energies 252 electron–lattice coupling 310 electron–lattice interactions 321 electron–phonon coupling 269 electron–phonon coupling constant 582 electron–phonon interactions 268, 293, 580 – Cs2 NaTmCl6 581 – LiTmF4 581 – NdBa2 Cu3 O7 582 – Pb2 Sr2 NdCu3 O8 582 – sodium disilicate glass:Eu3+ 581 electron–spin interactions 293 electronic speciﬁc heat coefﬁcient 8 emission – of Cm(III) 496 – of lanthanides 496 – of U(VI) 474, 496–498 energy back-transfer model 578, 579 energy diffusion process 574 energy levels under pressure 520, 527, 550 energy migration 573, 574 energy shifts of excited conﬁgurations 549 energy transfer between f elements 572, 573 – Eux La1−x P5 O14 574 – La2 O2 S:Eu3+ 574 – Ndx Y1−x P5 O14 572, 573 – Tbx Eu1−x P5 O14 574 – Tbx La1−x P5 O14 574 energy transfer from ligand states to f elements 569, 571 – Eu2 [Pt(CN)4 ]3 ·18H2 O 569 – Eu[Au(CN)2 ]3 ·3H2 O 570 – Eu[Au(CN)2 ]3 ·3H2 O 569 – rare-earth chelates 571 – Sm2 [Pt(CN)4 ]3 ·18H2 O 569 energy transfer from transition metal ions to f elements 574–577 – Cr3+ :Tm3+ :Y3 Al5 O12 575 energy transfer in insulators 572 energy transfer in semiconductors 577, 579 – GaAs:Er,O 580 – GaAs:Er3+ 578, 579 – GaP:Er3+ 580 – InP:Yb3+ 578, 580 – recover of quenched luminescence 579 – Si:Er3+ 580 energy transfer rate under pressure 576

641

642 enthalpies of dimerisation 198 – LnBr3 197, 198 – LnCl3 198 – LnF3 198 – LnI3 198 enthalpies of formation – LnBr3 173, 192 – LnCl3 173, 192, 194 – LnF3 173, 192, 193 – LnI3 173, 192 enthalpies of fusion – LnBr3 181 – LnCl3 179, 222 – LnF3 177, 178 – LnI3 181 enthalpies of sublimation – gaseous LnBr3 238 enthalpy increment – LaF3 162 – LnF3 164 enthalpy of formation 191 – CeX 3 (cr) 211 – DyX 3 (cr) 217 – ErX 3 (cr) 219 – EuX 3 (cr) 215 – GdX 3 (cr) 215 – HoX 3 (cr) 219 – LaX 3 (cr) 209 – LnBr3 172, 175 – LnCl3 172, 175 – LnF3 169, 171 – LnI3 172, 175 – LuX 3 (cr) 221 – NdX 3 (cr) 213 – PrX 3 (cr) 212 – SmX 3 (cr) 214 – TbX 3 (cr) 216 – TmX 3 (cr) 220 – YbX 3 (cr) 221 enthalpy of formation of gaseous – LnBr3 194 – LnCl3 193 – LnF3 191 – LnI3 196 enthalpy of sublimation – gaseous LnCl3 236 – gaseous LnF3 234 – gaseous LnI3 239 – LnBr3 195 – LnCl3 194

SUBJECT INDEX entropies of fusion – LnBr3 182 – LnCl3 180 – LnF3 177, 178 – LnI3 182 Er–Ag–Sb 88 Er–Au–Sb 89 Er–Cu–Sb 88 Er–M–Sb systems 88 Er–Ni–Sb 88 Er–Pd–Sb 88 Er–Pt–Sb 89 Er–Sb 37 Er–Zr–Sb 88 Er0.33 U0.67 Sb2 94 Er3 Au3 Sb4 89 Er3 Cu3 Sb4 88, 133 Er4 Sb3 39 Er5 Ni2 Sb 88 Er5 Pd2 Sb 88 Er5 Pt2 Sb 89 Er5 Sb3 39 ErAgSb2 88, 128 ErBa2 Cu3 Ox 524, 535 Er(C2 H5 SO4 )3 ·9H2 O 524 ErCl3 524 ErCuSb2 88, 119, 121 ErNi2−x Sb2 88 ErNiSb 88, 116, 118 ErPd2 Sb 88 ErPdSb 88 ErPtSb 89 ErSb 39 (ErSb)1−x Nix 88 ErSb2 (HT) 39 ErZrSb 88 ethylsulfate compounds 536 Eu benzoylacetonate 523 Eu–Ag–Sb 78 Eu–Au–Sb 78 Eu–Cu–Sb 77 Eu–Fe–Sb 76 Eu–Li–Sb 76 Eu–M–Sb systems 76 Eu–Mn–Sb 76 Eu–Ni–Sb 76 Eu–Os–Sb 78 Eu–Pd–Sb 77 Eu–Pt–Sb 78 Eu–Ru–Sb 77 Eu–Se–Sb 77

SUBJECT INDEX Eu–Sn–Sb 78 Eu–Te–Sb 78 Eu–Zn–Sb 77 Eu11 Sb10 39 Eu14 MnSb11 76, 111, 134 Eu16 Sb11 37, 39 Eu2 O3 523 Eu2 [Pt(CN)4 ]3 ·18H2 O 523 Eu2 Sb3 38 Eu2 Zn3 (NO3 )12 ·xH2 O 523 Eu3 GdSb3 94 Eu3 Se9 Sb4 77 Eu4 TeSb2 78 Eu5 Sb3 39 EuAgSb 78 Eu[Au(CN)2 ]3 ·3H2 O 523 EuAuSb 78 Eu(C2 H5 SO4 )3 ·9H2 O:Ce3+ 521 EuCu1.75 As2 95 EuCu1.75 As2 –EuCu2 Sb2 region 95 EuCu1.85 AsSb 95 EuCu1.8 As1.5 Sb0.5 95 EuCu1.9 As0.85 Sb1.15 95 EuCu2 As0.5 Sb1.5 95 EuCu2 As0.65 Sb1.35 95 EuCu2 As0.6 Sb1.4 95 EuCu2 Sb2 77, 95 EuCuSb 77 EuF2 523 EuFe4 P12 14, 23 EuFe4 Sb12 15, 24, 76 EuLiSb 76 EuMn2 Sb2 76 EuNi1.53 Sb2 99 EuNi2 Sb2 76 EuO 523 EuOCl 523 Eu(OH)3 523 EuOs4 Sb12 15, 78 EuP5 O14 523, 530 EuPd2 Sb2 77 EuPdSb 77 EuPO4 523 EuPtSb 78 EuRu4 P12 14, 24 EuRu4 Sb12 15, 24, 77 EuSb2 38 EuSe 523 EuSe4 Sb2 77 EuSn3 Sb4 78 EuTe–Sb2 Te3 section 78

643

EuTe4 Sb2 78 EuTe7 Sb4 78 EuVO4 523 EuZn2 Sb2 77 excess entropy 156 excess heat capacity 155 – DyF3 156 – LnCl3 167 exchange energy 260 exchange of 18 O for 16 O 305, 308 exchange striction 276, 277, 284 excited conﬁgurations under pressure 549, 567 – CsSmI3 549 – SrF2 :Sm2+ 549 excited states under pressure 548 expansion of wavefunctions 533, 535 experimental hyperﬁne shift 357 Fermi surface 9, 23 ferrimagnetic 24 – order 285 ferromagnet 24 ferromagnetic 21–24 – exchange interactions 270 – insulator 273 – interactions 25 – quantum critical point 17 – σ -bond superexchange 275 – superexchange 257, 267, 343 – superexchange interactions 262 – vibronic (FV) 287 ferromagnetic-ferromagnetic transition 316 ﬁeld-induced phase transition 25 ﬁgure of merit 27 ﬁlled skutterudite 1–32 – structure 4, 5 ﬂuctuating ferromagnetic phases 311 ﬂuctuating phases 333 fourfold symmetry 415, 448 free-ion parameters under pressure 530, 531 from vibronic to itinerant electronic behavior 333 FV phase 287, 317, 325 FV-FM transition 325 γ 12, 13, 17, 21, 22, 26 G-type antiferromagnetic order GaAs:Er3+ 524 gadolinium break 400, 459 GaP:Er3+ 525 Gd benzoylacetonate 524 Gd–Ag–Sb 81 Gd–Au–Sb 81

282, 283

644 Gd–Bi–Sb 82 Gd–Cr–Sb 79 Gd–Cu–Sb 80 Gd–Fe–Sb 79 Gd–Ge–Sb 80 Gd–Li–Sb 78 Gd–Li–Sb, isothermal section Gd–M–Sb systems 78 Gd–Ni–Sb 79 Gd–Pd–Sb 81 Gd–Pt–Sb 81 Gd–Sb 36 Gd–Se–Sb 80 Gd–Te–Sb 81 Gd–Zn–Sb 80 Gd–Zr–Sb 81 Gd0.32 U0.68 Sb2 94 Gd0.5 Sr0.5 MnO3 338 Gd1.5 U1.5 Sb7 94 Gd16 Sb39 37, 39 Gd2.31 U0.69 Sb7 94 Gd2 LiSb 78 Gd2 O2 S:Eu3+ 523, 534 Gd2 Sb5 37, 39 Gd2 Se3 –Sb2 Se3 section 80 Gd3 Au3 Sb4 81 Gd3 Cu3 Sb4 80, 132, 133 Gd3 Ga5 O12 :Nd3+ 521 Gd3 Li4 Sb4 78 Gd3 Sc2 Ga3 O12 :Nd3+ 521 Gd4 (Bix Sb1−x )3 82 Gd4 Li3 Sb4 78 Gd4 Sb3 39 Gd5 Ni2 Sb 80 Gd5 Pd2 Sb 81 Gd5 Pt2 Sb 81 Gd5 Sb3 39 Gd6 Ge4.3 Sb11.7 80 Gd6 Ge5−x Sb11+x 135 Gd6 ZnSb15 80, 133, 134 Gdx R5−x Sb3 94 (Gdx Sb1−x )2 Se3 80 GdAgSb2 81, 128 GdCrSb3 79 GdCu2 Sb2 80 GdCuSb2 80, 121 GdFe1−x Sb2 79 GdFe4 P12 15, 24 GdLi3 Sb2 78 GdLi7 Sb2 78 GdNi2−x Sb2 79

SUBJECT INDEX

78, 79

GdNi2 Sb2 79 GdNiSb 79, 116 GdNiSb2 79, 121 GdOBr:Eu3+ 523 GdOCl:Eu3+ 523 GdOCl:Pr3+ 521, 533, 537 GdPdSb 81, 118 GdPdSb2 81, 121 GdPtSb 81 GdRu4 P12 15, 25 GdSb (α) 39 GdSb (β) 39 GdSb2 37 GdSb2 (HT) 39 GdSb2 (LT) 39 GdSbTe 81 GdTe–Sb2 Te3 section 81 GdU2 Sb6 95 GdZn1−x Sb2 80 GdZrSb 81 geometrical factor 368, 372 geometrical parameters – Ln2 X 6 dimers 232 glasses under pressure 555 – 90B2 O3 –10Na2 O–1Eu2 O3 – coordination changes 556 – silicate glasses 556 – structural changes 556

555

H3 BO3 –LiF–Sm2 O3 522 Hall coefﬁcient 17 Hall measurements 8 Hall mobility 13 heat capacity 9, 11, 12, 16–18, 20–24, 26 – GdCl3 159 – LnF3 154 – LuCl3 159 heat capacity data 13 heat capacity of gaseous – LnBr3 182 – LnCl3 182 – LnF3 182 – LnI3 182 heat capacity of liquid – LnBr3 177, 180, 181 – LnCl3 177–179, 222 – LnF3 175, 177, 178 – LnI3 177, 180, 181 heavy-fermion 13 heavy-fermion state (HFS) 17 heavy-fermion superconductor 22 hexagonal polytypes 251, 277, 323

SUBJECT INDEX Hf5 CuSb3 -anti type 110 HfCuSb2 , structure type 139 HfCuSi2 , structure type 102, 138, 140 HFS 19 high pressure technique 517 high temperature heat capacity 162 – LnBr3 168, 169 – LnCl3 166, 169 – LnF3 165 – LnI3 168, 170 high-pressure ﬂuorescence line-narrowing 555 high-spin 253 Ho–Ag–Sb 87 Ho–Au–Sb 87 Ho–Cu–Sb 86 Ho–M–Sb systems 86 Ho–Ni–Sb 86 Ho–Ni–Sb, isothermal section 86 Ho–Pd–Sb 87 Ho–Pt–Sb 87 Ho–Sb 37 Ho–Zr–Sb 87 Ho0.33 U0.67 Sb2 94 Ho0.5 Sr0.5 MnO3 338 Ho1.47 U1.53 Sb7 94 Ho3 Au3 Sb4 87 Ho3 Cu3 Sb4 87, 133 Ho4 Sb3 39 Ho5 Ni2 Sb 86 Ho5 Pd2 Sb 87 Ho5 Pt2 Sb 87 Ho5 Sb3 39 HoAgSb2 87, 128 HoCl3 524 HoCuSb2 87, 121 HoMnO3 275 HoNi2−x Sb2 86 HoNiSb 86, 116, 118 HoNiSb2 86, 121 HoPd2 Sb 87 HoPdSb 87 HoPtSb 87 HoSb 39 HoSb2 39 HoZrSb 87 Hund intraatomic exchange 253 hybridization 12, 17 hydration number – of Cm(III) 479 – of lanthanides 479 hydration number (more speciﬁc) 475–483

645

hydrostatic limits 519 hyperﬁne interaction 359, 364, 377, 459 hyperﬁne paramagnetic lanthanide induced shift 357 hyperﬁne parameters 24 indirect exchange 258 inelastic neutron scattering 11, 22 inﬂuence of 4f N−1 5d1 conﬁgurations on intensities and lifetimes under pressure 563 inﬂuence of charge transfer states on intensities and lifetimes under pressure 567 inner-sphere relaxation 359 InP:Yb3+ 525 insulator-metal transition 287, 305 intensities under pressure 559 – rare-earth ethylsulfates 562 – rare-earth trichlorides 562 – rare-earth triﬂuorides 562 – UF3 562 – UF4 562 interatomic interactions 256, 260 interatomic spin–spin exchange interactions 256 intergrowth structures 250 intermediate valence 26 intraatomic electron–electron interactions 260 intraatomic exchange 286, 294 intraatomic interactions 252, 260 intrinsic parameters 542–546, 548 isomer shift 24 isotope effect 305 isotope exchange 262, 305, 306, 310, 327, 329 isotope shift 308 itinerant orbiton 269 itinerant-electron magnetism 259, 260 Jahn–Teller deformations 267, 311, 323 Jahn–Teller distortional 305 Jahn–Teller distortions 263, 266, 304, 307, 311, 343 Jahn–Teller energies 263 Jahn–Teller orbital ﬂuctuations 261 Jahn–Teller orbital ordering 263, 268, 306 Jahn–Teller ordering 262 Jahn–Teller site deformations 293 Jahn–Teller site distortions 255, 343 κmin 29, 30 κL 29 KHg2 structure type 108, 138 Kondo temperature 13

646 La–Ag–Sb 48 La–Al–Sb 43 La–Au–Sb 49 La–Cd–Sb 48 La–Co–Sb 44 La–Cr–Sb 43 La–Cu–Sb 45 La–Cu–Sb, isothermal section 45, 46 La–Fe–Sb 43 La–Ga–Sb 47 La–Ge–Sb 47 La–Hf–Sb 49 La–In–Sb 48 La–Li–Sb 42 La–M–Sb systems 42 La–Mg–Sb 42 La–Mn–Sb 43 La–Nb–Sb 47 La–Ni–Sb 44 La–Ni–Sb, isothermal section 45 La–Os–Sb 49 La–Pb–Sb 49 La–Pd–Sb 48 La–Pt–Sb 49 La–Rh–Ge 48 La–Ru–Sb 47 La–Sb 36 La–Sn–Sb 48 La–Ti–Sb 43 La–V–Sb 43 La–Zn–Sb 46 La–Zr–Sb 47 La0.1 Rh8 Sb24 48 (La0.25 Nd0.75 )0.7 Ca0.3 MnO3 306, 308 La0.4 Ce0.6 CuSb2 120 La0.5 Ca0.5 MnO3 259, 328 La0.5 Sr0.5 MnO3 337 La0.65 Ba0.35 MnO3 295 La0.7−x Prx Ca0.3 MnO3 290, 294, 309 La0.7−x Yx Ca0.3 MnO3 310 La0.75 Ca0.25 MnO3 299, 308 (La0.78 Pr0.22 )2/3 Ca1/3 MnO3 305 La0.7 Ca0.3 MnO3 298, 310 La0.7 (Ca1−y Sry )0.3 MnO3 294 La0.7 Sr0.3 MnO3 290, 294 La0.8 Ca0.2 MnO3 305 La1−x Bax Mn1−x Tix O3 267 La1−x Cax MnO3 295, 298, 307, 318, 323 La1−x Srx MnO3 260, 286, 311, 323, 326, 333 (La1−y Ndy )0.7 Ca0.3 MnO3 294 (La1−y Pry )0.67 Ca0.33 MnO3 327

SUBJECT INDEX (La1−y Pry )0.7 Ca0.3 MnO3 294 (La1−y Ry )0.7 A0.3 MnO3 290, 310 (La1−y Ry )0.7 Ca0.3 MnO3 310 (La1−y Ry )2/3 (Ca1−x Srx )1/3 MnO3 299 La12 Ga4 Sb23 47 La13 Ga8 Sb11 47 La13 Ga8 Sb21 structure type 104 La2/3 (Ca1−x Srx )1/3 MnO3 310 La2/3 Ca1/3 MnO3 299, 300 La2/3 Sr1/3 MnO3 295 La2 O2 S:Eu3+ 524 La2 O2 S:Tb3+ 524 La2 Sb 38 La3 Au3 Sb4 49, 129 La3 Cu3 Sb4 46, 133 La3 HfSb5 49 La3 InGe structure type 111 La3 Mg4.6 Sb6 43, 110 La3 Mg5−x Sb6 structure type 110 La3 NbSb5 47 La3 Sb2 38 La3 TiSb5 43, 110 La3 YSb3 94 La3 ZrSb5 47 La4.89 Mg1.539 Sb6 42, 110 La4 Mg4.48 Sb7 42, 110 La4 Mg5−x Sb7 structure type 110 La4 PbSb2 49 La4 Sb3 38 La4 SnSb2 48 La5−y Mg2−x Sb6 structure type 110 La5/8−x Prx Ca3/8 MnO3 327 La5/8−y Pry Ca3/8 MnO3 340 La5 Pb3 Sb 49 La5 Sb3 38 La6 Co13 Sb 44 La6 CuSb15 46 La6 Ge2.8 Sb13.2 47 La6 Ge5−x Sb11+x 135 La6 Ge5−x Sb11+x structure type 103 La6 MnSb15 43 La6 MnSb15 structure type 103, 138, 140 La6 ZnSb15 47 LaAg2 Sb2 113 LaAgSb2 48, 128 LaAuSb2 49, 121 La(C2 H5 SO4 )3 ·9H2 O:Gd3+ 524 La(C2 H5 SO4 )3 ·9H2 O:Nd3+ 521 La(C2 H5 SO4 )3 ·9H2 O:Pr3+ 521 LaCdSb2 48 LaCl3 536, 537

SUBJECT INDEX LaCl3 :Nd3+ 522, 531, 536 LaCl3 :Pr3+ 521, 528, 531, 536, 538, 541 LaCl3 :U3+ 531, 536 LaCo1−x Sb2 44 LaCrSb3 43 LaCu0.82−0.87 Sb2 46 LaCu2 Sb2 113 LaCu6 Sb3 46 LaCuSb2 120, 121 LaF3 :Nd3+ 522 LaFe1−x Sb2 43 LaFe4 As12 9, 14 LaFe4 P12 8, 9, 14 LaFe4 P12 structure type 95 LaFe4 Sb12 9–11, 14, 44 LaFe4 Sb12 structure type 138 LaGaO3 277 LaGaSb2 47 LaIn0.8 Sb2 48 LaInSb2 structure type 102 LaLi3 Sb2 42 LaLi3 Sb2 structure type 96 LaMn0.5 Ga0.5 O3 292, 294, 303, 329 LaMn0.65−0.76 Sb2 43 LaMn0.87 Sb2 120 LaMn1−x Alx O3 273 LaMn1−x Gax O3 267, 284 LaMn1−x Gax O3 and LaMn1−x Scx O3 269 LaMn1−x Scx O3 268 LaMnO3 256, 262, 277, 280–282, 284, 294, 323, 333 LaMnO3+δ 285, 317 LaMnO3−δ 317 LaMSb2 119 La(Ni, Sb)4 141 LaNi1.51 Sb2 45, 99 LaNi2 Sb2 45, 98, 113 LaNiSb 44, 106, 115, 116 LaNiSb2 45, 121 lanthanide antimonides 7 lanthanide arsenides 7 lanthanide contraction 184 lanthanide (III) halides 147–247 lanthanide induced relaxation 356, 359 lanthanide phosphides 6 lanthanide-induced contact relaxation 359 lanthanide-induced Curie-spin relaxation 362 lanthanide-induced dipolar relaxation 361 lanthanum trihalides 198 LaOBr:Eu3+ 523 LaOCl:Eu3+ 523

LaOCl:Pr3+ 521, 533, 537 LaOs4 As12 9, 14 LaOs4 P12 9, 14 LaOs4 Sb12 12, 14, 49 LaOX:Eu3+ 534 LaPd2 Sb2 48 LaPdSb 48 LaPdSb2 48, 121 LaPt2 Ge2 141 LaPt2 Ge2 structure type 100 LaPtSb 49 LaRh2 Sb2 48 LaRhSb 48, 95 LaRu4 As12 9, 10, 14 LaRu4 P12 8, 14 LaRu4 Sb12 12, 14, 47 LaSb 38 LaSb (HP) 38 LaSb2 38 LaSnx Sb2 49 LaSnx Sb2 (x = 0.75) structure type 103 LaSnSb2 142 lattice constant 26 lattice thermal conductivity 11 LaVSb3 43 LaZn0.6 Sb2 47 LaZn1−x Sb2 46 LaZnSb2 102 lifetime – non-radiative 467, 468, 475–478 – of Cm(III) 472, 495 – of lanthanides 471–474, 481, 482, 494, 495 – of U(VI) 471–474, 484, 485, 494, 495 – radiative 467, 468, 472, 481 lifetimes under pressure 559, 565 – CaFCl:Sm2+ 565 – Gd2 O2 S:Tb3+ 566 – La2 O2 S:Tb3+ 566 – SrFCl:Sm2+ 563–565 LiGaGe, structure type 139, 140 ligand–ligand interactions 544, 545 ligand-ﬁeld wavefunctions 254 ligand-ﬁelds 253 LiNbO3 :Er3+ 525 line shifts under pressure 527–529 – LaCl3 :Pr3+ 527 – LaCl3 :U3+ 529 LIR 356, 359 LIS 357, 362, 373, 375 LiTmF4 525

647

648

SUBJECT INDEX

Ln–X equilibrium bond distances – LnBr3 184 – LnCl3 184 – LnF3 184 – LnI3 184 Ln2 Cl6 dimers 193 Ln2 X 6 dimers 190, 197 LnCl3 158 LnF3 149, 154, 162 LnX 3 monomers 182 local distortions 540, 541, 543, 544, 555 – MFCl:Sm2+ 541 – RCl3 540 – ROCl:Pr3+ 541 local distortions from high-pressure experiments 540 local structure 555 local structure in glasses 555 local vibrations 581 local-density approximation (LDA) 12 localized from itinerant electronic behavior 330 localized to itinerant electronic behavior 330 localized to itinerant electronic transition 282 long-range orbital order 263, 269 low temperature heat capacity 154, 158 – LnBr3 161 – LnI3 161 Lu–Ag–Sb 93 Lu–Au–Sb 93 Lu–Cu–Sb 93 Lu–M–Sb systems 92 Lu–Ni–Sb 92 Lu–Pd–Sb 93 Lu–Pt–Sb 93 Lu–Sb 37 Lu–Zr–Sb 93 Lu3 Au3 Sb4 93 Lu3 Sb 39 Lu5 Ni2 Sb 92 Lu5 Pd2 Sb 93 Lu5 Pt2 Sb 93 Lu5 Sb3 39 LuAgSb 93 LuCuSb2 93 luminescence inhibition 485, 486, 489–492 luminescence lines under pressure 527 luminescence quantum yield 468, 495, 496 luminescence quenching 563, 572 LuNiSb 92, 116 LuPtSb 93 LuSb 39

LuSb2 39 LuZrSb 93 Madelung energy 252 magnetic anisotropy 368–370, 373, 377 magnetic polaron 293 magnetic polarons 323 magnetic susceptibility 8–10, 12, 13, 15, 17, 20–23, 25, 26 magnetic susceptibility tensor 366 magnetic transition 23 magnetization 19, 25, 26 magnetoresistance 290, 293, 299 magnon scattering 22 mass enhancement 26 material property database 200 mean bond energy – LnBr3 195, 196 – LnCl3 194 – LnF3 193, 195 – LnI3 197 melting temperature 150, 151 – CnBr3 152 – LnBr3 151, 206 – LnCl3 151, 203 – LnF3 151, 200 – LnI3 151, 208 metal to insulator transition 23 metal–insulator transition (M-I) 19 metamagnetic 17, 25, 329, 340 metamagnetic transition 340 metamagnetism 326, 337, 340 MFCl:Sm2+ 537 MgAgAs structure type 109, 139 MgCu2 Al, structure type 139 mixed valence 24 mixing of conﬁgurations 561 mixing of f- and d-orbitals by lattice vibrations 562 mixing of ligand and 4f states 561 mixing of wavefunctions 563, 564, 567 mixing with excited conﬁgurations 567 MnCu2 Al structure type 101 MnO6/2 octahedra are rotated 323 Mo5 B2 Si structure type 111, 139 mobilities 28 model-free method 376, 380, 443, 453, 459 molar volume – LnBr3 161 – LnCl3 159 – LnF3 159 – LnI3 161

SUBJECT INDEX molecular geometry 182 – of the Ln2 X 6 dimer 190 molecular structure 183 – Ln2 X 6 190 molecular vibrations Ln2 X 6 191 monometallic lanthanide complexes Mössbauer 8, 13, 24 Mössbauer isomer shift 24 Mott–Hubbard transition 260 MR 299 multiple sites under pressure 555 – GaAs:Er3+ 555 – LiNbO3 :Er3+ 555 MYX compounds 532, 537

380

Na2 O–2SiO2 :Eu3+ (glass) 524 Na5 Eu(MoO4 )4 524 Na5 Eu(WO4 )4 524 narrow gap semiconductor 13 (Nd, Pr)2 Sb 93 (Nd, Pr)4 Sb3 93 (Nd, Pr)Sb 93 (Nd, Pr)Sb2 93 Nd–Ag–Sb 69 Nd–Ag–Sb, isothermal section 69, 70 Nd–Au–Sb 71 Nd–Au–Sb, isothermal section 71, 72 Nd–Cd–Sb 69 Nd–Cd–Sb, isothermal section 69, 70 Nd–Co–Sb 65 Nd–Co–Sb, isothermal section 65, 66 Nd–Cr–Sb 62 Nd–Cr–Sb, isothermal section 62, 63 Nd–Cu–Sb 67 Nd–Cu–Sb, isothermal section 67 Nd–Fe–Sb 63 Nd–Fe–Sb, isothermal section 63–65 Nd–Ga–Sb 68 Nd–Ge–Sb 68 Nd–Hf–Sb 71 Nd–In–Sb 70 Nd–Li–Sb 62 Nd–M–Sb systems 62 Nd–Mn–Sb 63 Nd–Mn–Sb, isothermal section 63, 64 Nd–Ni–Sb 66 Nd–Ni–Sb, isothermal section 66, 67 Nd–Os–Sb 71 Nd–Pd–Sb 69 Nd–Pt–Sb 71 Nd–Rh–Ge 69

Nd–Ru–Sb 69 Nd–Sb 36 Nd–Sn–Sb 70 Nd–Te–Sb 71 Nd–Ti–Sb 62 Nd–V–Sb 62 Nd–Zn–Sb 67 Nd–Zn–Sb, isothermal section 67, 68 Nd–Zr, Nb–Sb 69 (Nd0.125 Sm0.875 )0.5 Sr0.5 MnO3 341 Nd0.33 U0.67 Sb2 94 Nd0.475 Pr0.475 Sb0.05 93 Nd0.5 (Ca0.5−x Crx )MnO3 336 Nd0.5 Ca0.5 MnO3 336 Nd0.5 Ca0.5 MnO3+δ 336 Nd0.5 Sr0.5 MnO3 326, 337 Nd0.7 Sr0.3 MnO3 308 Nd12 Ga4 Sb23 68 Nd26 Mn8 Sb66 63 Nd29 Mn13 Sb58 63 Nd2 Fe17 65 Nd2 Sb 38 Nd2 Te3 –Sb2 Te3 section 71 Nd3 Au3 Sb4 72 Nd3 Cu3 Sb4 67, 132, 133 Nd3 HfSb5 71 Nd3 NbSb5 69 Nd3 TiSb5 62 Nd3 ZrSb5 69 Nd4 Sb3 38 Nd5 Sb3 38 Nd6 CdSb15 69 Nd6 CoSb15 66 Nd6 Fe13 Sb 65, 104 Nd6 Fe13 Si structure type 104, 138 Nd6 Ge3.6 Sb12.4 68 Nd6 Ge5−x Sb11+x 135 Nd6 ZnSb15 68 Nd8+x Sb19+y 37, 38 NdAgAs2 structure type 102 NdAgSb2 69, 128 NdAgSb2 structure type 138 NdAuSb2 72, 121 NdBa2 Cu3 O7 522 NdBr3 522 Nd(C2 H5 SO4 )3 ·9H2 O 522 NdCdSb 69 NdCdSb2 69 NdCl3 522, 531 NdCl3 ·6H2 O 522 NdCo1−x Sb2 66

649

650 NdCo3 Sb2 66 NdCrSb3 62 NdCu6 Sb3 67 NdCuSb2 67, 121 NdF3 522 NdFe0.6 Sb2 64 NdFe1−x Sb2 63 NdFe2−x Sb2 65 NdFe2 Sb2 142 NdFe2 Sb2 structure type 100 NdFe3 Sb2 65, 97, 142 NdFe3 Sb2 structure type 96 NdFe4 As12 14, 23 NdFe4 P12 14, 22 NdFe4 Sb12 14, 23, 63 NdIn0.8 Sb2 70 NdLi2 Sb2 62 NdMn0.83 Sb2 120 NdMn1−x Sb2 63 NdMnO3 252 NdNi2 Sb2 66 NdNiSb 66, 116 NdNiSb2 66, 121 NdOs4 As12 14, 23 NdOs4 P12 14, 23 NdOs4 Sb12 14, 23, 71, 95 NdP5 O14 522 NdPd2 Sb2 69 NdPdSb 69, 106 NdPdSb2 69, 121 NdPtSb 71 NdPtSb (or LiGaGe) structure type 107 NdRh2 Sb2 69 NdRhSb 69, 108 NdRu4 As12 14, 23 NdRu4 P12 14, 23 NdRu4 Sb12 14, 23, 69 NdSb 38 NdSb2 38 NdSbTe 71 NdSnx Sb2 70 NdTe3 Sb 71 NdVSb3 62 NdZn1−x Sb2 68 NdZn2 Sb2 68 nephelauxetic effect 529, 535 neutron scattering 17, 23 neutron scattering under pressure 535 non-Fermi liquid (NFL) 15 nonradiative crossover between conﬁgurations nonradiative energy transfer 567, 569

SUBJECT INDEX nonradiative energy transfer to charge transfer states 567 nonradiative transfer to excited conﬁgurations 566 NOTA 410 nuclear relaxation 358, 363, 448 nuclear relaxation in paramagnetic lanthanide complexes 358 18 O substitution for 16 O 308 18 O/16 O exchange 305, 307, 309 O* –R transition 323 O* -orthorhombic to the R-rhombohedral

564

319 octaethylporphyrin 448 odd crystal-ﬁeld terms under pressure 566, 567 ODS 19 on-site coulomb energies 260 one-nucleus method 376, 445, 456 OO phase 328 optical measurements 17, 26 optical studies under pressure 515–589 orbital and charge disorder 290 orbital and charge order 290, 315 orbital and charge ordering 259, 315, 321, 332 orbital and/or bond-length ﬂuctuations 288 orbital and/or phase ﬂuctuations 338 orbital angular momentum 318 orbital degeneracy 253 orbital disorder 263, 270, 321 orbital exciton 269 orbital ﬂuctuations 256, 257, 261, 263, 266, 284, 285, 289, 293, 304, 315, 321, 332, 336, 343 orbital order 325, 332, 333, 335 orbital order and disorder 329 orbital order–disorder transition 263 orbital ordering 255, 267–269, 288, 308, 311, 328, 330, 332, 335, 343 orbitally disordered 273 orbitally ﬂuctuating 272, 287, 290, 321 orbitally ordered 272 orbitally ordered Jahn–Teller state 268 orbitally ordered state 315 orbitally-correlated crystal ﬁelds 547 orbitals ﬂuctuate 272 orbiton 268, 269 order–disorder transitions 311, 335 ordering of the Mn(III) e orbitals 310 orthorhombic Pbnm symmetry 251 orthorhombic to rhombohedral to tetragonal to cubic 322 oxydiacetic acid 381 oxygen interstitials 251 oxygen stoichiometry 251, 265, 323, 328

SUBJECT INDEX oxygen vacancies 282 oxygen-deﬁcient 277 oxygen-stoichiometric 268, 269, 276 pair-density-function analysis 261, 263 paramagnetic NMR lanthanide included shifts 353–463 Pauli exclusion principle 256 Pauli susceptibility 13 Pb2 Sr2 NdCu3 O8 522 PDF 304 percolate 309 percolating 294, 326 percolation 293, 296, 298, 301, 309, 312, 324, 325, 327, 339 percolation threshold 270 perovskite 3 phase diagram 19 phase ﬂuctuations 304, 321, 328 phase segregation 324 phase transitions detected by f elements 557 phase transitions under pressure 556, 558 – Eu(OH)3 558 – sesquioxides 557 phonon drag 303 phonon sidebands under pressure 581 – BaFCl:Sm2+ 581 phonon–glass 30 phtalocyanine 440 polaron 300, 308, 336 polaron conduction 335 polaronic 298, 305, 308, 325, 326 polaronic conduction 257, 286, 294 polaronic phase 310 polaronic to itinerant-electron behavior 304 polaronic to itinerant/vibronic 299 polymetallic lanthanide complexes 444 polymorphism 149 – in the lanthanide tribromides 153 – in the lanthanide trichlorides 152 – in the lanthanide triﬂuorides 150 – in the lanthanide triiodides 153 – LnBr3 152 – LnCl3 150 – LnI3 152 potential energy curves 185 power generation 27 Pr–Ag–Sb 61 Pr–Au–Sb 62 Pr–Cd–Sb 61 Pr–Co–Sb 59

Pr–Cr–Sb 58 Pr–Cu–Sb 59 Pr–Fe–Sb 59 Pr–Ga–Sb 60 Pr–Ge–Sb 60 Pr–Hf–Sb 62 Pr–In–Sb 61 Pr–Li–Sb 58 Pr–M–Sb systems 58 Pr–Mn–Sb 58 Pr–Ni–Sb 59 Pr–Os–Sb 62 Pr–Pd–Sb 61 Pr–Pt–Sb 62 Pr–Rh–Sb 60 Pr–Ru–Sb 60 Pr–Sb 36 Pr–Sn–Sb 61 Pr–Te–Sb 61 Pr–Ti–Sb 58 Pr–V–Sb 58 Pr–Zn–Sb 60 Pr–Zr, Nb–Sb 60 Pr0.33 U0.67 Sb2 94 Pr0.5 (Ca0.25 Sr0.75 )0.5 MnO3 342 Pr0.5 Ca0.35 Sr0.15 MnO3 338 Pr0.5 Ca0.5 MnO3 336 Pr0.5 (Ca0.5 Sr0.5 )0.5 MnO3 342 Pr0.5 (Ca0.85 Sr0.15 )0.5 MnO3 338 Pr0.5 (Ca1−x Srx )0.5 MnO3 332 Pr0.5 Sr0.5 MnO3 336, 337 Pr0.5 (Sr0.9 Ca0.1 )0.5 MnO3 335 Pr0.7 Ca0.3 MnO3 290, 294 Pr12 Ga4 Sb23 60 Pr12 Ga4 Sb23 structure type 104 Pr2/3 Ca1/3 MnO3 305 Pr2 Sb 38 Pr3 Au3 Sb4 62 Pr3 Cu3 Sb4 60, 133 Pr3 HfSb5 62 Pr3 NbSb5 60 Pr3 Pt3 Sb4 62, 129 Pr3 TiSb5 58 Pr3 ZrSb5 60 Pr4 Sb3 38 Pr5/8 Ca3/8 MnO3 327 Pr5 Sb3 38 Pr6 Fe13 Sb 59 Pr6 Ge5−x Sb11+x 60, 135 Pr6 ZnSb15 60, 133, 134 PrAgSb2 61, 128

651

652 PrAuSb2 62, 121 PrBr3 521 Pr(C2 H5 SO4 )3 ·9H2 O 521 PrCd1−x Sb2 61 PrCdSb2 61 PrCl3 521, 531 PrCo1−x Sb2 59 PrCrSb3 58 PrCu2 Sb2 60, 113 PrCuSb2 60, 119, 121 pressure 9 pressure sensor 518, 552–554 – rare-earth sensors 552 – ruby 518, 519, 552 – SrB4 O7 :Sm2+ 554 – SrFCl:Sm2+ 554 – YAG:Eu3+ 553 – YAG:Nd3+ 553 – YAG:Sm3+ 553 – YAlO3 :Nd3+ 552 pressure-generation with diamond anvils PrF3 521 PrFe1−x Sb2 59 PrFe4 As12 14, 21 PrFe4 P12 14, 17–19 PrFe4 Sb12 14, 21, 59 PrIn0.8 Sb2 61 PrLi2 Sb2 58 PrMn0.82 Sb2 58, 120 PrMnO3 294 PrNi1.8 Sb2 113 PrNi2−x Sb2 59 PrNi2 Sb2 59, 100, 113 PrNiSb 59, 116 PrNiSb2 59, 121 Pr(NO3 )3 ·6H2 O 521 PrO2 521 PrOCl 521, 537 PrOCl:Pr3+ 533 PrOs4 As12 14, 21 PrOs4 P12 14, 20 PrOs4 Sb12 14, 21, 22, 62 PrPd2 Sb2 61 PrPdSb 61, 118 PrPdSb0.952 61 PrPdSb2 61, 119, 121 PrPtSb 62 PrRh2 Sb2 61 PrRhSb 60, 118 PrRu4 As12 14, 21 PrRu4 P12 14, 19, 20

SUBJECT INDEX PrRu4 Sb12 14, 21, 60 PrSb 38, 521, 535 PrSb2 38 PrSnx Sb2 61 PrTeSb 61 PrVSb3 58 PrX (X = N, P, As, Sb, S, Se) 521 PrZn1−x Sb2 60 pseudo-contact shift 366, 367 pseudo-gap 17 QCP behavior 333 quadrupolar order 17 quantum chemical computations 182 quantum critical behavior at a QCP 343 quantum critical point 15, 332 quantum-critical-point ﬂuctuations 261 quaternary systems 95

518

(R, U)3 Sb7 94 (R,U)Sb2 94 R–Cu(Ag, Au)–Sb, peculiarities of interaction 139 R–d-element–Sb, peculiarities of interaction 137 R–f-element–Sb, peculiarities of interaction 140 R–Fe(Co, Ru, Rh, Os, Ir)–Sb, peculiarities of interaction 137 R–Mn(Cd, Zn)–Sb, peculiarities of interaction 137 R–Ni(Pd, Pt)–Sb, peculiarities of interaction 138 R–p-element–Sb, peculiarities of interaction 136 R–R –Sb systems 93 R–s-element–Sb, peculiarities of interaction 136 R–Sb binary compounds 37 R–Sb systems, peculiarities of interaction 135, 136 R–Ti(V, Cr, Zr, Nb, Mo, Hf, Ta, W, Re)–Sb, peculiarities of interaction 137 R–U–Sb 94 R–U–Sb systems 94 R0.5 A0.5 MnO3 327, 330 R0.5 Sr0.5 MnO3 337 R0.7 A0.3 MnO3 310 R11 Sb10 136 [R 2 (L14 –2H)3 ] 444 [R 2 (L15 –2H)3 ] 448 R2 O2 S:Eu3+ 530 R2 Sb 136 R2 Sb5 136 R3 Au3 Sb4 129 [R 3 (L16 –3H)2 (OH2 )6 ]3+ 454 [R 3 (L17 )3 ]9+ 455 R4 Sb3 136

SUBJECT INDEX R5 Sb3 136 R6 Ge5−x Sb11+x 133 Raman measurements 20 Raman modes 23 rare earth – antimony systems 35–146 rare earth – manganese perovskites 249–351 rare-earth compounds studied under pressure 521 rattlers 29 RbCaF3 :Gd3+ 524 RbCdF3 :Gd3+ 524 [R(benzyl-EDTA)] 373, 374 RCl3 530–532 [RCo(L5 )3 ]5+ 400 [RCo(L5 )3 ]6+ 396 redox energy 252, 260 reduced enthalpy increment – CeCl3 168 – GdCl3 166 – LaCl3 167 – PrCl3 168 – PrF3 164 reduction of free-ion parameters 529, 533 reduction of Slater parameter 529, 532 reduction of the free-ion parameters 529 reduction of the spin–orbit coupling parameter 529 refractive index under pressure 561, 563, 564 refrigeration 28 Reilley’s method 376 ReO3 4 representations of base vectors 259 resistivity 8–10, 12, 13, 15–18, 20–22, 24–26 resonance energy transfer 571 resonance integrals 253 rhombic system 379, 455, 459 ¯ symmetry 251 rhombohedral R 3c [R(indole-EDTA)] 373, 374 [R(L1 –2H)3 ]3− 381 [R(L10 –4H)]− 419, 437 [R(L11 )]3+ 374, 426, 437 [R(L12 –8H)]5− 430, 437 [R(L13 –2H)2 ]− 440 [R(L2 )3 ]3+ 384 [R(L2a )3 ]3+ 385 [R(L3 )3 ]3+ 387, 410 [R(L4 +H)]4+ 390 [R(L4 )]3+ 390 [R(L6 )]3+ 401 [R(L7 –2H)3 ]3− 404, 406 [R(L7a –2H)3 ]3− 405 [R(L7b –2H)3 ]3− 405 [R(L7c –2H)3 ]3− 406

[R(L8 –3H)] 410 [R(L9 –H)4 ]− 415 r(Ln–X) bond length – LnBr3 184 – LnCl3 184 – LnF3 184 – LnI3 184 [RM(L5 )3 ]5/6+ 393 RMnO3 275 ROCl:Pr3+ 537, 539 ROY :Eu3+ 537 RSb 136 RSb2 136 [R(texa)X2 ] 374, 375 Ruddlesden–Popper 250 Ruddlesden–Popper phases [RZn(L5 )3 ]5+ 393

653

251

Sb2 Te3 –Dy2 Te3 section 85 Sb2 Te3 –Sb3 Yb4 section 92 Sb2 Te3 –Sm2 Te3 section 75 Sb2 Te3 –SmTe section 75 Sb2 Te3 –TeYb section 92 Sb2 Te3 –Yb section 92 Sb2 Te4 Yb 92 Sb4 Te7 Yb 92 Sb4 Te7 Yb–Te section 92 Sb4 Te7 Yb–Yb section 92 Sc–Co–Sb 37 Sc–M–Sb systems 37 Sc–Ni–Sb 37 Sc–Pt–Sb 40 Sc2 Sb 38 Sc5 Sb3 38 scanning calorimetry 23 ScCoSb 37 Schottky heat capacity 154 Schottky peak 22 ScNiSb 37, 109, 118 ScPtSb 40 ScSb 38 Seebeck 24 Seebeck coefﬁcient 10, 13, 17 segregation of orbitally disordered and orbitally ordered volumes 289 semicovalent component of the superexchange 284 semicovalent exchange 256, 277 sensitized luminescence 483, 484, 494, 506–509 separation of contact and pseudo-contact contributions 372 Si:Er3+ 525

654 single conﬁgurational coordinate energy level diagram 564, 568 skutterudite 2 Slater parameters under pressure 529 Sm–Ag–Sb 75 Sm–Au–Sb 76 Sm–Cd–Sb 75 Sm–Co–Sb 73 Sm–Cr–Sb 72 Sm–Cu–Sb 73 Sm–Fe–Sb 72 Sm–Ga–Sb 74 Sm–Ge–Sb 74 Sm–Hf–Sb 75 Sm–M–Sb systems 72 Sm–Mn–Sb 72 Sm–Nb–Sb 74 Sm–Ni–Sb 73 Sm–Os–Sb 76 Sm–Pd–Sb 74 Sm–Pt–Sb 76 Sm–Ru–Sb 74 Sm–Sb 36 Sm–Se–Sb 74 Sm–Sn–Sb 75 Sm–Te–Sb 75 Sm–Ti–Sb 72 Sm–V–Sb 72 Sm–Zn–Sb 73 Sm0.33 U0.67 Sb2 94 Sm0.5 Sr0.5 MnO3 338 Sm12 Ga4 Sb23 74 Sm2 Fe17 73 Sm2 [Pt(CN)4 ]3 ·18H2 O 523 Sm2 Sb 38 Sm2 Sb5 37, 38 Sm2 SnSb3 75 Sm3 Au3 Sb4 76 Sm3 Cu3 Sb4 73, 133 Sm3 GdSb3 94 Sm3 HfSb5 75 Sm3 NbSb5 74 Sm3 NdSb3 94 Sm3 Se9 Sb4 74 Sm3 TiSb5 72 Sm4 Sb3 38 Sm5 Sb3 38 Sm6 Fe13 Sb 72 Sm6 Ge5−x Sb11+x 74, 135 Sm6 ZnSb15 74, 133, 134 SmAgSb2 75, 128

SUBJECT INDEX small polarons 283, 285, 294, 307, 311, 323 small to Zener polarons 308 small-polaron/Zener-polaron 308 SmAuSb2 76, 121 Sm(C2 H5 SO4 )3 ·9H2 O 523 SmCdSb2 75 SmCo1−x Sb2 73 SmCuSb2 73, 121 SmFCl 522 SmFe1−x Sb2 72 SmFe4 P12 14, 23 SmFe4 Sb12 14, 23, 72 SmGaSb2 74 SmMn0.90 Sb2 72, 120 SmNi2 Sb2 73 SmNiO3 277 SmNiSb 73, 106, 116 SmNiSb2 73, 121 SmOs4 Sb12 14, 23, 76 SmPd2 Sb2 75 SmPdSb 74 SmPdSb2 74, 121 SmPtSb 76 SmRu4 P12 14, 23 SmRu4 Sb12 14, 23, 74 SmS 522 SmSb 38 SmSb2 38 SmSbTe 75 SmSe 522 SmSnx Sb2 75 SmTe3 Sb 75 SmTe4 Sb2 75 SmTe7 Sb4 75 SmVSb3 72 SmZn1−x Sb2 73 speciﬁc heat 15 spherical coordinates 367 spherical tensor operators 368 spin canting 283, 310 spin conﬁgurations 258, 259 spin expectation value 362, 365 spin ﬂuctuations 288 spin orbit 365 spin ordering 269 spin waves 319, 321 spin–orbit coupling parameter under pressure 529 spin–phonon coupling 284 spin-canted antiferromagnet 285 spin-correlated crystal ﬁelds 547, 548 – MFCl:Sm2+ 548

SUBJECT INDEX spin-density wave (SDW) 260 spin-dependent resonance integrals 256 spin-glass 270, 273, 285, 289, 290, 303, 312, 340 spin-glass insulator 273 spin-glass phase transforms to a ferromagnetic phase 273 spin-glass to a ferromagnetic phase 272 spin-independent resonance integrals 256 spin-lattice interactions 276, 321 spinodal phase segregation 261, 262, 282, 289, 290, 292, 316, 323, 328 spiral-spin conﬁguration 275, 276 Sr1−x Cax MnO3 (0 x 1) and Sr1−y Bay MnO3 (0 y 0.2) 278 SrAl2 O4 :Eu2+ 523 SrB4 O7 :Sm2+ 522 SrBPO5 :Eu2+ 523 SrF2 :Er3+ 525 SrF2 :Eu3+ 524 SrF2 :Pr3+ 521 SrF2 :Sm2+ 522 SrF2 :Tm2+ 525 SrFCl0.5 Br0.5 :Sm2+ 522 SrFCl:Sm2+ 522 SrFe4 Sb12 15 SrMnO3 277 SrOs4 Sb12 15 SrRu4 Sb12 15 stability constant – of Cm(III) 499, 500, 505, 506 – of lanthanides 499, 504, 505 – of U(VI) 499–501, 505 stability constant (general) 501, 502 standard entropy 154, 158 – EuX 3 162 – LaX 3 162 – LnBr3 161, 163 – LnCl3 157, 159 – LnF3 157, 158 – LnI3 161, 163 – LuX 3 162 standard molar entropies 156 stripes 304 strong-correlation ﬂuctuations 262 structural parameters – LnBr3 229 – LnCl3 227 – LnF3 224 – LnI3 230 structural transition 20

655

sublimation enthalpies – LnBr3 196 – LnF3 192, 195 – LnI3 196, 197 superconducting 9, 12, 21 superconductivity 8, 9 superconductor 21 superexchange 256, 279, 280, 333 superexchange interaction 259, 268, 276, 277, 317, 343 superexchange interatomic interactions 307 superparamagnetic 296, 324, 335, 343 superparamagnetism 296, 332 superposition model 539, 541, 546, 547 – LaCl3 :Nd3+ 542 – LaCl3 :Pr3+ 542 – LaCl3 :U3+ 542 – MFCl:Sm2+ 542 – ROCl:Pr3+ 542 supramolecular 355, 358, 359, 361, 363, 366, 459 symmetry-restricted covalency model SRC 530, 533 synthesis and crystal growth 6 t2g 5 &D 9, 12, 13, 17, 21 TJT 319 TOO = orbital-ordering temperature 321 TOR = orthorhombic-rhombohedral transition temperature 321 t = tolerance factor 339 Tb–Ag–Sb 83 Tb–Au–Sb 84 Tb–Cr–Sb 82 Tb–Cu–Sb 82 Tb–Ge–Sb 83 Tb–Li–Sb 82 Tb–M–Sb systems 82 Tb–Ni–Sb 82 Tb–Pd–Sb 83 Tb–Pt–Sb 83 Tb–Sb 36 Tb–Te–Sb 83 Tb–Zn–Sb 83 Tb–Zr–Sb 83 Tb0.33 U0.67 Sb2 94 Tb0.5 Sr0.5 MnO3 338 Tb1.5 U1.5 Sb7 94 Tb2 Sb5 37, 39 Tb3 Au3 Sb4 84 Tb3 Cu3 Sb4 82, 133 Tb4 Sb3 (α) 39

656

SUBJECT INDEX

Tb5 Ni2 Sb 82 Tb5 Pd2 Sb 83 Tb5 Pt2 Sb 83 Tb5 Sb3 39 Tb6 Ge5−x Sb11+x 83, 135 Tb3+ in solutions 524 TbAgSb2 83, 124, 128 TbCrSb3 82 TbCuSb2 82, 121 TbLi2 Sb2 82 TbNi2−x Sb2 82 TbNiSb 82, 116 TbNiSb2 82, 121 TbP5 O14 524, 536 TbPdSb 83 TbPdSb2 83, 119, 121 TbPtSb 83 TbRu4 P12 15, 25, 26 TbSb2 (HT) 39 TbSb2 (LT) 39 TbSb(α) 39 TbTe–Sb2 Te3 section 83 TbZn1−x Sb2 83 TbZrSb 83 Te2 Ag3 Tl structure type 109 ternary antimonides with the equiatomic composition 140 ternary antimonides with the R:Sb ratio equal to 1:2 141 ternary antimonides, interconnection with binary structure types 140 tetragonal I4/mcm symmetry 251 thermal conductivity 13 thermal expansion 20 thermoelectric couple 28 thermoelectric generator 31 thermoelectric properties 2, 13, 24, 26 ThFe4 P12 15 ThOs4 As12 15 three-nuclei method 379 threefold symmetry 381, 444, 454 ThRu4 P12 15 tight-binding 267 tight-binding bandwidth 260, 262, 292 time-resolved emission spectroscopy 465–514 TiNiSi structure type 109, 138–140 TlCdF3 :Gd3+ 524 Tm–Ag–Sb 90 Tm–Au–Sb 90 Tm–Cu–Sb 89 Tm–M–Sb systems 89

Tm–Ni–Sb 89 Tm–Pd–Sb 89 Tm–Pt–Sb 90 Tm–Sb 37 Tm–Zr–Sb 89 Tm0.33 U0.67 Sb2 94 Tm3 Au3 Sb4 90 Tm5 Ni2 Sb 89 Tm5 Pd2 Sb 89 Tm5 Pt2 Sb 90 Tm5 Sb3 39 TmAgSb2 90, 123, 128 TmCl3 525 TmCuSb2 89, 121 TmNiSb 89, 116, 118 TmPdSb 89 TmPtSb 90 TmSb 39 TmSb2 39 TmSe 525 TmTe 525 TmZrSb 89 tolerance factor 250, 261, 275, 277, 287, 290, 292–294, 299, 305, 308–311, 322, 323, 325, 326, 330, 332, 333, 342 trace detection 508 – of Cm(III) 507, 508 – of lanthanides 507, 508 – of U(VI) 507, 508 transition at TJT 323 transition from a spin glass to a ferromagnetic phase 270 transition from antiferromagnetic to ferromagnetic behavior 292 transition from ferromagnetic insulator (FI) to ferromagnetic metal (FM) 316 transition from localized e to 1D itinerant 330 transition from localized to itinerant electronic behavior 260, 268, 304, 315, 332 transition from localized-electron to band magnetism 281 transition from polaronic to itinerant electronic behavior 312 transition from the FM toward the FV state 325 transition from vibronic to itinerant electronic behavior 316 transition temperature 150, 151 – LnBr3 151, 206 – LnCl3 151, 203 – LnF3 151, 200 – LnI3 151, 153, 208

SUBJECT INDEX transitions under pressure – trihalide compounds 558 transport gap 12 trimetallic lanthanide complexes 453 triple-decker dimetallic compound 449 tris{2-[N -methylcarbamoyl-(6-(N ,N diethylcarbamoyl)pyridine-2)ethyl]amine} 390 two-manganese (Zener) polarons 283 two-nuclei method 377, 446 two-phase ﬂuctuations 321, 327, 332 type G 276 type-A AFM phase 322, 335–337 type-A antiferromagnetic 310, 315, 330, 333 type-A antiferromagnetic order 264, 268 type-A (CAFI) 322 type-A canted-spin antiferromagnet 270 type-A magnetic order 311 type-C antiferromagnetic order 323, 330 type-CE 332 type-CE AFI phase 327, 328, 330 type-CE antiferromagnetic phase 288, 326, 332, 339 type-CE antiferromagnetic-insulator (AFI) 326 type-CE phase 326, 327 U3 CrSb5 structure type UFe4 P12 15

110, 137

Van Vleck 368 Van Vleck paramagnetism 23 vapour pressure – LnBr3 194 – LnCl3 193 – LnI3 196 vapour pressures 191 variance 251, 278, 332, 333, 337, 338, 342 vibrational density of states 11 vibrational frequencies – Ln2 X 6 compounds 233 – LnBr3 190, 229 – LnCl3 186, 188, 189, 227 – LnF3 186, 187, 189, 224 – LnI3 190, 230 vibrational properties 182 vibrational spectra 183 vibronic 304, 310, 311, 321, 325, 343 – bandwidth 308, 311 – conduction 292, 293, 333 – conductor 266, 315 – ferromagnetic phase 310

657

– ferromagnetic superexchange 307 – (FV) clusters 323 – isotropic superexchange 267 – Mn(III)–O–Mn(III) superexchange interaction 272 – phase 310 – state 308 – superexchange 257, 265–267, 289, 292–294, 310, 315, 317, 321 vibronic to itinerant 315 vibronic-itinerant electronic transition 316 vibrons 329 virial theorem 261, 282, 290, 308, 310, 330, 332 weak canted-spin ferromagnetism 264 weak ferromagnetic component 285 weak ferromagnetism 258 Wilson–Sommerfeld ratio 13, 26 X–Ln–X bond angle – LnBr3 185 – LnCl3 185 – LnF3 185 – LnI3 185 X–Ln–X equilibrium bond angles – Ln 184 – LnBr3 184 – LnCl3 184 – LnF3 184 – LnI3 184 XANES 12, 13, 20, 24, 26 Y–Ag–Sb 42 Y–Au–Sb 42 Y–Cu–Sb 41 Y–Li–Sb 40 Y–M–Sb systems 40 Y–Ni–Sb 40 Y–Ni–Sb, isothermal section Y–Pd–Sb 41 Y–Pt–Sb 42 Y–Sb 36 Y–Te–Sb 42 Y–Zr–Sb 40 Y1−x Ux Sb 94 Y2 O2 S:Eu3+ 524 Y2 O3 :Eu3+ 524 Y3 Al5 O12 553 Y3 Al5 O12 :Eu3+ 524 Y3 Al5 O12 :Nd3+ 522 Y3 Al5 O12 :Sm3+ 523 Y3 Al5 O12 :Tb3+ 524

40–42

658 Y3 Al5 O12 :Tm3+ 525 Y3 Au3 Sb4 42 Y3 Au3 Sb4 structure type 106, 140 Y3 Cu3 Sb4 41, 132, 133 Y3 Sb 38 Y4 Sb3 38 Y5 Nix Sb3−x 41 Y5 Pd2 Sb 42 Y5 Pt2 Sb 42 Y5 Sb3 37 Y5 Sb3 (HT) 38 Y5 Sb3 (LT) 38 YAgSb2 42, 128 YAlO3 553 YAlO3 :Nd3+ 522 Yb–Ag–Sb 92 Yb–Al–Sb 90 Yb–Au–Sb 92 Yb–Cd–Sb 91 Yb–Cu–Sb 91 Yb–In–Sb 92 Yb–Li–Sb 90 Yb–M–Sb systems 90 Yb–Mn–Sb 90 Yb–Ni–Sb 90 Yb–Pd–Sb 91 Yb–Pt–Sb 92 Yb–Sb 37 Yb–Se–Sb 91 Yb–Te–Sb 92 Yb–Zn–Sb 91 Yb11 Sb10 39 Yb14 AlSb11 90, 135 Yb14 MnSb11 90, 135 Yb14 ZnSb11 91, 134, 135 Yb3 DySb3 94 Yb3 GdSb3 94 Yb4 Sb3 39 Yb5 In2 Sb6 92, 111 Yb5 Sb3 39 YBa2 Cu3 O7 :Pr3+ 521 YbAgSb 92, 118, 119 YbAuSb 92, 118, 119 YbCd2 Sb2 91

SUBJECT INDEX YbCuSb 91, 118, 119 YbCuSb2 91 YbFe4 Sb12 15, 16, 26, 27 YbLiSb 90 YbMn2 Sb2 90 YbNiSb 90, 118 YbO 525 YbOs4 Sb12 15 YbPd2 Sb 91 YbPdSb 91, 118 YbPtSb 92 YbS 525 YbSb 39 YbSb2 39 YbSe4 Sb2 91 (YbTe)x (Te3 Sb2 )1−x 92 YbZn2 Sb2 91, 98 Y(C2 H5 SO4 )3 ·9H2 O:Ce3+ 521 Y(C2 H5 SO4 )3 ·9H2 O:Nd3+ 522 YCrO3 277, 280, 281 YCuSb2 41, 119, 121 YLi3 Sb2 40, 142 YNiSb 41 YP5 O14 :Nd3+ 522 YPd2 Sb 41, 101 YPdSb 41 YPtSb 42 YSb 38 YSb2 38 YTe3 Sb 42 YVO4 :Eu3+ 524 YZrSb 40, 108 Zener double exchange 292, 315, 317, 332 Zener pairs 328, 330, 332 Zener polarons 258, 283, 285, 294, 300, 308, 309, 311, 323, 325, 328, 329, 332, 335, 338, 339, 343 Zener to small polarons 300 Zener two-manganese polarons 285 Zintl compounds 5 ZnS:Eu2+ 523 ZrBeSi structure type 106, 139, 140 ZT 13, 26–30